We often hear the word resonance: “public resonance”, “event that caused resonance”, “resonant frequency”. Quite familiar and ordinary phrases. But can you say exactly what resonance is?

If the answer jumped out at you, we are truly proud of you! Well, if the topic “resonance in physics” raises questions, then we advise you to read our article, where we will talk in detail, clearly and briefly about such a phenomenon as resonance.

Before talking about resonance, you need to understand what oscillations are and their frequency.

Oscillations and Frequency

Oscillations are a process of changing the states of a system, repeated over time and occurring around an equilibrium point.

The simplest example of oscillation is riding on a swing. We present it for a reason; this example will be useful to us in understanding the essence of the phenomenon of resonance in the future.

Resonance can only occur where there is vibration. And it doesn’t matter what kind of fluctuations they are - fluctuations electrical voltage, sound vibrations, or simply mechanical vibrations.

In the figure below we describe what fluctuations can be.

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Oscillations are characterized by amplitude and frequency. For the swings already mentioned above, the oscillation amplitude is the maximum height to which the swing flies. We can also swing the swing slowly or quickly. Depending on this, the oscillation frequency will change.

Oscillation frequency (measured in Hertz) is the number of oscillations per unit time. 1 Hertz is one oscillation per second.

When we swing a swing, periodically rocking the system with a certain force (in this case, the swing is an oscillatory system), it performs forced oscillations. An increase in the amplitude of oscillations can be achieved if this system is influenced in a certain way.

By pushing the swing at a certain moment and with a certain periodicity, you can swing it quite strongly, using very little effort. This will be a resonance: the frequency of our influences coincides with the frequency of oscillations of the swing and the amplitude of the oscillations increases.

The essence of the phenomenon of resonance

Resonance in physics is a frequency-selective response of an oscillatory system to a periodic external influence, which manifests itself in a sharp increase in the amplitude of stationary oscillations when the frequency of the external influence coincides with certain values ​​characteristic of a given system.

The essence of the phenomenon of resonance in physics is that the amplitude of vibrations increases sharply when the frequency of influence on the system coincides with the natural frequency of the system.

There are known cases when the bridge along which soldiers were marching resonated with the marching step, swayed and collapsed. By the way, this is why now, when crossing the bridge, soldiers are supposed to walk at a free pace, and not in step.

Examples of resonance

The phenomenon of resonance is observed in a variety of physical processes. For example, sound resonance. Let's take a guitar. The sound of the guitar strings itself will be quiet and almost inaudible. However, there is a reason that the strings are installed above the body - the resonator. Once inside the body, the sound from the vibrations of the string intensifies, and the one who holds the guitar can feel how it begins to slightly “shake” and vibrate from the blows on the strings. In other words, resonate.

Another example of observing resonance that we encounter is circles on water. If you throw two stones into the water, the passing waves from them will meet and increase.

The action of a microwave oven is also based on resonance. In this case, resonance occurs in water molecules that absorb microwave radiation (2.450 GHz). As a result, the molecules resonate, vibrate more strongly, and the temperature of the food rises.

Resonance can be both beneficial and harmful. And reading the article, as well as the help of our student service in difficult educational situations, will only bring you benefit. If, while completing your coursework, you need to understand the physics of magnetic resonance, you can safely contact our company for quick and qualified help.

Finally, we suggest watching a video on the topic “resonance” and making sure that science can be exciting and interesting. Our service will help with any work: from an essay on “The Internet and Cybercrime” to a coursework on the physics of oscillations or an essay on literature.

Quite often, to build a welding inverter, the main three types of high-frequency converters are used, namely converters connected according to the following circuits: asymmetric or oblique bridge, half-bridge, and full bridge. In this case, resonant converters are subtypes of half-bridge and full-bridge circuits. According to the control system, these devices can be divided into: PWM (pulse width modulation), PFM (frequency control), phase control, and there may also be combinations of all three systems.

All of the above converters have their pros and cons. Let's deal with each one separately.

Half bridge system with PWM

The block diagram is shown below:

This is perhaps one of the simplest, but no less reliable push-pull converters. The “surge” of the voltage of the primary winding of the power transformer will be equal to half the supply voltage - this is a drawback of this circuit. But if you look from the other side, you can use a transformer with a smaller core without fear of entering the saturation zone, which is also a plus. For welding inverters with a power of about 2-3 kW, such a power module is quite promising.

Since power transistors operate in hard switching mode, drivers must be installed for their normal operation. This is due to the fact that when operating in this mode, transistors require a high-quality control signal. It is also necessary to have a no-current pause in order to prevent the simultaneous opening of transistors, which will result in the failure of the latter.

Quite a promising view of a half-bridge converter, its circuit is shown below:

A resonant half bridge will be a little simpler than a PWM half bridge. This is due to the presence of resonant inductance, which limits the maximum current of transistors, and switching of transistors occurs at zero current or voltage. The current flowing through the power circuit will be in the form of a sine wave, which will remove the load from the capacitor filters. With this design of the circuit, drivers are not necessarily needed; switching can be carried out by a conventional pulse transformer. The quality of control pulses in this circuit is not as significant as in the previous one, but there should still be a no-current pause.

In this case, you can do without current protection, and the shape of the current-voltage characteristic is , which does not require its parametric formation.

The output current will be limited only by the magnetizing inductance of the transformer and, accordingly, can reach quite significant values ​​in the event that a short circuit occurs. This property has a positive effect on the ignition and burning of the arc, but it also must be taken into account when selecting output diodes.

Typically, the output parameters are adjusted by changing the frequency. But phase regulation also provides some advantages and is more promising for welding inverters. It allows you to bypass such an unpleasant phenomenon as the coincidence of a short circuit with resonance, and also increases the range of regulation of output parameters. The use of phase control can allow the output current to be varied in the range from 0 to I max.

Asymmetrical or oblique bridge

This is a single-ended, forward-flow converter, the block diagram of which is given below:

This type of converter is quite popular both among ordinary radio amateurs and among manufacturers of welding inverters. The very first welding inverters were built precisely according to such schemes - an asymmetric or “oblique” bridge. Noise immunity, a fairly wide range of output current regulation, reliability and simplicity - all these qualities still attract manufacturers to this day.

Quite high currents passing through transistors, an increased requirement for the quality of the control pulse, which leads to the need to use powerful drivers to control transistors, and high requirements for installation work in these devices and the presence of large pulse currents, which in turn increase the requirements for - These are significant disadvantages of this type of converter. Also, to maintain normal operation of the transistors, it is necessary to add RCD chains - snubbers.

But despite the above disadvantages and the low efficiency of the device, an asymmetric or “oblique” bridge is still used in welding inverters. In this case, transistors T1 and T2 will operate in phase, that is, they will close and open simultaneously. In this case, energy accumulation will occur not in the transformer, but in the inductor coil Dr1. That is why, in order to obtain the same power with a bridge converter, double the current through the transistors is required, since the duty cycle will not exceed 50%. More details this system we'll look at it in future articles.

It is a classic push-pull converter, the block diagram of which is shown below:

This circuit allows you to receive power 2 times more than when turning on the half-bridge type and 2 times more than when turning on the “oblique” bridge type, while the magnitudes of the currents and, accordingly, losses in all three cases will be equal. This can be explained by the fact that the supply voltage will be equal to the “drive” voltage of the primary winding of the power transformer.

In order to obtain the same power with a half-bridge (drive voltage 0.5U supply), the current required is 2 times! less than for the half-bridge case. In a full bridge circuit with PWM, the transistors will operate alternately - T1, T3 are on, and T2, T4 are off and, accordingly, vice versa when the polarity changes. The values ​​of the amplitude current flowing through this diagonal are monitored and controlled. To regulate it, there are two most commonly used methods:

• Leave the cut-off voltage unchanged, and change only the length of the control pulse;
• Carry out changes in the cut-off voltage level according to data from the current transformer while leaving the duration of the control pulse unchanged;

Both methods can allow changes in the output current within fairly large limits. A full bridge with PWM has the same disadvantages and requirements as a half bridge with PWM. (See above).

It is the most promising high-frequency converter circuit for a welding inverter, the block diagram of which is shown below:

A resonant bridge is not much different from a full PWM bridge. The difference is that with a resonant connection, a resonant LC circuit is connected in series with the transformer winding. However, its appearance radically changes the process of power transfer. Losses will decrease, efficiency will increase, the load on input electrolytes will decrease and electromagnetic interference will decrease. In this case, drivers for power transistors should be used only if MOSFET transistors are used that have a gate capacitance of more than 5000 pF. IGBTs can only get by with a pulse transformer. More detailed descriptions of the schemes will be given in subsequent articles.

The output current can be controlled in two ways - frequency and phase. Both of these methods were described in a resonant half-bridge (see above).

Full bridge with dissipation choke

Its circuit is practically no different from the circuit of a resonant bridge or half-bridge, only instead of a resonant LC circuit, a non-resonant LC circuit is connected in series with the transformer. Capacitance C, approximately C≈22μF x 63V, works as a balancing capacitor, and the inductive reactance of the inductor L as a reactance, the value of which will change linearly depending on the change in frequency. The converter is controlled by frequency. , As the voltage frequency increases, the inductance resistance will increase, which will reduce the current in the power transformer. Quite a simple and reliable method. Therefore, a fairly large number of industrial inverters are built according to this principle of limiting output parameters.

On August 14 of this year, a road bridge in Genoa collapsed; according to the latest data, 42 people became victims of the disaster. While engineers and investigators are figuring out why and how this happened, Around the World decided to remember and list the main possible reasons bridge collapses and notable examples of such collapses from the past.

Humanity began to build bridges more than three thousand years ago, which allows the bridge to lay claim to honorary title itself Moreover, many bridges built thousands of years ago - especially by the Romans, who achieved amazing heights in the field of bridge construction - are still standing and even performing their functions.

But, like any engineering structure, the bridge can collapse, which has often happened over the past three thousand years. And it’s also good if it’s right in the process of construction. It’s worse if this happens after the work is completed.

Why are bridges being destroyed? Often there can be several reasons at the same time, and they, successfully complementing each other, lead to disaster. For example, the engineer made the calculations incorrectly, the builders skimped on materials or violated construction technologies, then the bridge was not operated correctly and, in the end, when a train that was too heavily loaded or large number cars or people collapsed in bad weather. However, in most cases one of the reasons acts as the main one.

Design and operation errors and excessive wear

Perhaps errors in design can be called the primary reason for the destruction of all engineering structures - bell towers, fortress walls or bridges. Moreover, the problem may appear immediately, or under certain conditions after construction is completed. This is what happened, for example, with a railway bridge over the Firth of Tay in Scotland in 1879. Engineer Thomas Bautsch, the author of the project and knighted for him, did not take into account the wind load when creating the project and planned the supports that supported the bridge trusses to be too thin. Added to this is the poor quality of materials and work. As a result, during a severe storm (10 out of 12 on the Beaufort scale) on the evening of December 28, 1879 (two years after construction was completed), a train with 75 people drove onto the bridge and soon found itself in the water: the spans of the longest bridge in the world at that time ( about 3000 meters) collapsed into the river along with the carriages and the locomotive.

This is what the bridge looked like a few weeks after the collapse. Today its structures have been dismantled, but the remains of the supports are still visible

But users of the suspension road bridge across the Tacoma Narrows between the city of Tacoma in Washington State (USA) and the Kitsup Peninsula were luckier. Problems with this long and rather elegant structure became known already at the construction stage: workers erecting the bridge noticed that when a side wind rose in the strait, the road surface began to vibrate and bend. For this they even nicknamed the bridge “Galloping Gertie” (Gallping Gertie). This, however, did not prevent the construction from being completed and the bridge being inaugurated on July 1, 1940. Moreover, although the vibrations of the road surface in the wind were noticeable to the naked eye and immediately began to cause concern among engineers, inspectors of regulatory authorities and drivers, the bridge was considered completely safe. Simultaneously with its operation, solutions to the problem were developed. What was the problem? The fact is that during the construction, advanced at that time solid carbon steel beams were used, on top of which the road surface was laid. If more conventional through beams were used, the wind blowing across the bridge would pass through them, and the solid beams would deflect air flows above and below and thus set the roadway in motion. Projects to correct the deficiency did not even have time to be fully thought through: on November 7 of the same year, 1940, the wind in the strait rose to strong, but not catastrophic, 18 m/s (about 64 km/h; 8 points on the Beaufort scale), and the bridge was at the end could not stand it at the end: the cables burst and the road surface, along with the car of the driver who miraculously escaped, fell into the strait; One dog died when it accidentally ran onto the bridge. And we received unique footage - he took it local resident, who happened to be at the bridge with a camera that day.

Resonance One of the most well-known causes of bridge destruction, although not the most common, is resonance, that is, the phenomenon of a sharp increase in the amplitude of vibrations of a system (in our case, the bridge structure) under periodic external influence. At school, this phenomenon is even explained in physics lessons, citing as an example the story of how a detachment of soldiers, walking in step, can cause a bridge to collapse. In fact, two reasons converge here: errors in design and improper operation; Sometimes bad weather can also be involved. This is exactly what happened with the Tacoma Narrows Bridge mentioned above. Resonance is often cited as the cause of the collapse of the Egyptian chain bridge in St. Petersburg on February 2, 1905, when the Life Guards Horse Grenadier Regiment was following, although the commission that investigated the causes of the incident indicated that the low quality of the iron of the chain was to blame Unfortunately, not all disasters of this kind occur without loss of life. The record death toll was the destruction due to the resonance of the suspension bridge over the Maine River in the city of Angers in central France on April 16, 1850, when more than 200 soldiers were killed walking across the bridge in a thunderstorm and strong winds. And one of the first recorded cases of this kind was the collapse of the Broughton Bridge in England near Manchester 19 years earlier. Then no one died, although two dozen of the 74 soldiers were injured when falling into the water, and a team appeared in the army break step(“go out of step”), used when crossing bridges, especially suspension bridges, which are more susceptible to resonance. The soldiers in Angers, by the way, carried out such a command, but this did not save them from trouble.

Exceeding the permissible load

Strictly speaking, exceeding the permissible load is also a violation of operating rules, although, as a rule, it is not a consequence of neglect of such rules and common sense motives as untimely repairs or carrying out repairs in violation of regulations (which destroyed the 710-meter bridge across the river in 2011 Mahakam in the Indonesian part of the island of Borneo), but by coincidence. This is exactly how we can evaluate, for example, what happened at 17:00 local time on Friday, December 15, 1967 with the Silver Bridge (Silver Bridge) across the Ohio River, connecting the states of Ohio and West Virginia. The bridge, built in 1928, was part of the highway U.S. Route 35 and enjoyed great popularity, which was reflected in the fact that a dense traffic flow regularly passed through it. In the weeks leading up to the holidays, traffic increased even more than usual, and the tragedy occurred on a Friday evening ten days before Christmas. The bridge collapsed due to the destruction of one of the suspension rods that attached the road surface to the cables, and behind it the rest of the bridge structures began to collapse - the entire destruction took about a minute. As a result, 46 people died.

The most accurate list of those killed in the bridge collapse in Dixon, Illinois, includes 46 names, and 37 of them were women, that is, 80%. Moreover, 19 of the dead were under 21 years of age. The reason for this disproportion is that women and children were allowed to go ahead so that they could better see the baptism ceremony in the waters of the river - precisely on that side walkway where the largest mass was concentrated. Heavy dresses, people falling from above and the structures of the ill-fated bridge completed the job.

Another example is also from America - from the city of Dixon, Illinois. The beginning of May 1874 was warm and sunny, so the pastor of the local Baptist church decided to hold a baptism ceremony in the waters of the Rock River for six new members of the community on the first Sunday of the month, the 4th. The convenient location was near the bridge, and such ceremonies usually attracted the attention of the townspeople (there were few alternative entertainment options in a provincial town with a population of just over 4,000 people in 1874). The bridge was built five years earlier and had a popular lattice design that was new for those years, which made it possible to assemble long crossings from short metal parts and, therefore, spend less money and build bridges in hard-to-reach areas.

On Sunday morning, between 150 and 200 people gathered on the bridge, all dressed for Sunday, with the largest number of people concentrated at one end of the bridge and within the boundaries of one span. The pastor took a theatrical pause before immersing the baptized person in the waters of the river. Suddenly, in the ensuing silence, a loud creaking sound was heard, and the bridge span began to fall along with the people gathered on it (men, women in heavy dresses with crinolines and petticoats, children, including small ones), who flew into the water from a height of more than five meters. About 50 people died. Officially, the cause of the incident was the design of the bridge, but the tragedy would not have occurred if it had not been overloaded, and unevenly.

Warfare and terrorism

In all the cases described above, bridges were destroyed due to unintentional actions of people. But this does not always happen; often people destroy crossings built by other people. Most often in human history this has happened during wars, and the largest number of bridges were destroyed in the 20th century during World War II by airstrikes or shelling - either to stop the advance of troops or to disrupt the economic activities of the enemy. Thus, the Hohenzollern Bridge, built in 1907–1911 in the center of Cologne, allowed road and rail transport and pedestrians to cross the Rhine and was therefore considered the most important element infrastructure of the Third Reich - during the war it was the busiest railway bridge in Germany. It is not surprising that since 1942 the Allies have been trying to destroy it with air raids. However, they were never able to completely disable it from the air - the bridge collapsed into the waters of the Rhine only on March 6, 1945, when it was blown up by American sappers.

The Hohenzollern Bridge, destroyed two months before the end of the war (pictured in the center) began to be restored shortly after the end of hostilities in Germany. And in 1948, railway traffic along it was already launched. The car line was put on a different route, and to the left and right of the tracks there are now pedestrian and bicycle paths, which offer magnificent views of the city in general and Cologne Cathedral in particular.

However, even after the end of World War II, bridges continued to be destroyed by air bombing and explosions - this fate befell, for example, the very beautiful cable-stayed Liberty Bridge in the Serbian city of Novi Sad in 1999 during the NATO war. military operation against Yugoslavia (the bridge, however, was restored in 2005).

Bridge collapses in literature The bridge often became a hero literary works, and some of them described the destruction of the crossing. So, the second Scottish poet half of the 19th century century, William McGonagall wrote the poem “The Wreck of the Bridge over the River Tay”, which we talked about above. The poem is famous for being considered one of the worst poems in the history of British literature. The writer Archibald Cronin in his novel “Castle Brodie” describes this event, although in prose, but much better. However, writers do not necessarily have to describe things that actually happened. For example, main character one of the best and most popular novels by Ernest Hemingway “For Whom the Bell Tolls” (eighth place in the list of one hundred best novels XX century, according to the French edition Le Monde) Robert Jordan joins a detachment of Spanish partisans just to blow up a strategically important bridge (spoiler: he blows it up and dies), moreover, the author claimed that all the events in the novel are fictitious. However, the greatest attention to the collapse of the bridge is perhaps given in the novel by the American writer Thornton Wilder, “The Bridge of Saint Louis,” written in 1927. The story centers on the collapse of a century-old suspension bridge built by the Incas in Peru on the road between Lima and Cuzco in 1714 just as five strangers were passing across it; they all died. The witness to the misfortune, the Franciscan monk Juniper, on whose behalf the story is told, is investigating why exactly these people ended up on the bridge at that unfortunate moment. The Incas built suspension bridges from strong vines and wood over rivers and gorges. Despite being unreliable (from a modern point of view) appearance, such bridges withstood the passage of not only people, but loaded lamas, and with proper care and timely repairs they served for centuries

Natural disaster

This category of causes includes floods and sudden sharp rises in water that simply wash away a bridge or destroy its supports and the soil underneath them, as well as earthquakes and landslides. It was the latter that caused the collapse of the bridge over the Pfeiffer Canyon (98 meters deep) on Highway 1 in California in March 2017. Over the course of a month, more than 1,500 mm of rain fell in the area of ​​the bridge, which caused the displacement of a thick layer of soil on the slope of the canyon along with the bridge support dug into this slope. Fortunately, there was no one on the bridge at that moment.

The 92-meter-high bridge over the Kinza River partially collapsed after encountering a tornado in 2003. Before its collapse, it was 625 meters long, making it the 4th tallest bridge in the United States. In 1977, the structure was included in the US National Register of Historic Places, and in 1982 - in the List of US Historic Civil Engineering Landmarks

Another, albeit rather exotic, scenario is a tornado. It was he who destroyed the famous railway bridge over the Cilantro River in Pennsylvania (USA) - a monument of engineering, built in 1883 and served until 1963, and then became the main attraction of the park Kinzua Bridge State Park. And on July 21, 2003, a tornado hit the park, hit the bridge and knocked down 11 of its 20 supports - the 120-year-old structures could not withstand wind speeds above 150 km/h.

Collision

A great way to bring down a bridge is to crash into it, and for the greatest success of this undertaking, it is worth aiming at the support. Although you can, if you wish, try to demolish the span, for example, by rushing under the bridge to vehicle greater height than the span itself. It must be said that in most cases the bridge wins (see the so-called “Bridge of Fools” in St. Petersburg), but not always, as happened with the Almö bridge, which connected the Swedish island of Cörn with the mainland. This beautiful arched structure (at the time of its construction the longest bridge of its type in the world) spanned a busy waterway and stood for 20 years without incident, until on a dark foggy night from January 17 to 18, 1980, it met a bulk carrier MS Star Clipper. He, following in difficult navigation conditions, passed not in the center of the arched span, touched the arch and demolished it. The road surface and bridge structures fell onto the ship's bridge and destroyed it. It is noteworthy that no one was injured on the ship. But, unfortunately, there were no casualties at all: in the fog, several cars drove at full speed onto the bridge from the direction of Chern and, not noticing that there was no bridge, fell from it into the icy waters of the strait - eight people died. There could have been more casualties if the truck driver coming from the continent had not noticed that the barriers had suddenly disappeared and did not have time to brake a meter from the cliff, blocking the road.

When a barge collides with a highway bridge I-40 in 2002, in the United States, no one was directly injured by the impact, but eight cars and three trucks managed to fall into the water - 14 people were killed, 11 were injured

And yet, a more reliable way to demolish a bridge is to crash into a support and preferably at full speed, as the loaded barge did Robert Y. Love in the Kerr Reservoir on the Arkansas River in Oklahoma, USA. Her helmsman collapsed at the helm, and the out-of-control vessel crashed into one of the road bridge's supports and carried it off, causing the collapse of a 177-meter section of the span. As in the case of the Almö bridge, the victims of the crash were car drivers who did not have time to brake on the edge (this happened on a May morning).

Photo: Wikimedia Commons, Stephen Lux/Getty Images, Posnov/Getty Images

Everywhere and every day we are accompanied by oscillatory systems in our lives.
The first impression in life is a swing. In this by no means simplest example, one can observe the dependence of the period of oscillation on the weight of the person swinging, as well as the problem of the movement of the swing being in phase with the external swinging force. Next comes an introduction to musical instruments, one way or another using various kinds of oscillatory systems to produce musical sounds. Well, and in the end, all the electronics that completely embrace us, the main and indispensable unit of which is a quartz resonator - a refined oscillatory system, so to speak.
And at the same time, do we understand so much about this...
The clearest definition of an oscillatory system was given by Lord Kelvin when he discovered electric L-C oscillatory circuit in 1878. Having discovered that when an impact is applied to an oscillatory circuit, a sinusoidal (harmonic) damping process occurs, Kelvin stated that this is proof that a new, previously unknown oscillatory system is taking place.
Thus, we can formulate that an oscillatory system is a device that has a mechanism for converting impact into a harmonic damping process.
But what is interesting is that we cannot apply this definition to all known and used oscillatory systems. This happens because for these devices, which are definitely oscillatory systems (according to Kelvin’s definition), the mechanism itself for transforming the shock into a sinusoid is not always known.
Regarding various types of pendulums, springs and oscillatory circuits, then the mechanisms of their oscillations are studied and considered. However, there are oscillatory systems whose mechanism is unknown, despite their very wide application. Thus, until recently it remained unknown how, say, quartz resonators play the role of an oscillatory system.
The quartz resonator effect was discovered back in 1917, but for some reason they were embarrassed to admit its incomprehensibility. Due to this shyness, a model of a quartz resonator was proposed in the form of its equivalent to a certain combination of several virtual capacitors and inductors. For some reason this kind of modeling is called a scientific description of quartz resonators, it’s all called theory, and this kind of scientific and educational literature exists apparently and invisibly.
It is clear that there are no virtual or real capacitors in quartz resonators, and all this scientific waste paper has nothing to do with these resonators. The fact is that in practice the frequency of a quartz resonator f 0 is determined by the thickness of the quartz plate h, and in its manufacture the following empirical formula is used:

f 0 = k / h, where (1)

k - technological coefficient.
So, in all the existing literature on quartz resonators, we will not find any mention of this empirical relationship, or any information at all about the connection between the natural frequency of the resonator and the dimensions of the plate.
60 years after the discovery of the properties of quartz plates, in 1977, it was discovered that not only quartz plates, but also objects from the vast majority of solid media (metals and alloys, glass, ceramics, rocks) are resonators. It turned out that the number of natural frequencies of these resonators is equal to the number of their sizes. So, a solid ball, say, made of glass, has only one size - diameter d, and, accordingly, one natural frequency f 0 , the connection between which, as it turns out, is determined by relation (1). A plate having a thickness h and sizes a And b, has three natural frequencies, each of which is related to the corresponding size by relation (1).
The presence of resonant properties of the objects listed above is revealed very simply, and even in several ways. In mine conditions, in the case of layered rocks, the simplest method is to press an elastic vibration field sensor (seismic receiver) to the object under study (roof rocks) and apply a short blow to the roof surface. The response to the impact will appear as a decaying harmonic signal. In laboratory conditions, this method is unacceptable, since it is very difficult to obtain the required impact parameters for small samples. In the laboratory, it turned out to be easier to use ultrasonic testing of the sample.
As it turned out, the resonant properties of a quartz resonator are not something unique and depend on the presence of the piezoelectric effect. The presence of the piezoelectric effect only simplifies the indication and use of this property. Thus, when studying the resonant properties of a piezoceramic disk, during the experiment it can be heated to a temperature exceeding the Curie point, at which the piezoelectric effect disappears, and its resonant properties will not change in any way.
However, if the scientists who studied quartz resonators managed to avoid searching for the physics of their resonant properties, then I had to take it seriously. The fact is that, despite the actually existing resonant manifestations, based on general considerations, a plate made of a homogeneous material should not exhibit resonant properties. Such a plate should not have a mechanism for converting the impact into a harmonic signal.
It cannot be said that this point of view is wrong, because there are materials from which objects are not resonators. Indeed, in materials such as plexiglass (plexiglass) and some others, this mechanism is absent. Plexiglas objects are not resonators. When impacted on a plexiglass plate, the reaction takes the form of a sequence of damped short pulses. That is, it fully complies with the provisions of generally accepted acoustics of solid media.
At the same time, as it turned out (in 1977), rock layers exhibit resonant properties, and using relation (1) it turned out to be possible to determine the structure of the rock mass without drilling (!). Well, it is clear that it is very difficult to use a physical effect even though it is not difficult to prove the impossibility of its existence. In addition, the use of this effect in mines made it possible to create a methodology for predicting the collapse of roof rocks - a phenomenon that accounts for 50% of injuries to miners throughout the world. But it was completely impossible to introduce into practice a technique based on such a dubious physical effect.
It took 4 years to find the difference between plexiglass and those materials from which objects are resonators. And somewhere in 1981, it was discovered that there is a difference, and it concerns the acoustic properties of the border zones of the vast majority of solid media.
It turned out that the acoustic properties of near-surface zones of media, objects from which exhibit the properties of resonators, are such that the speed of propagation of the front V fr during normal sounding it is not constant, and decreases as the front approaches the surface.
Figure 1 shows the case of normal sounding of a resonator plate 1 thick h. Addiction V fr (x), as well as minimum and maximum values V fr and zone sizes Δ h obtained from measurements made on many plates of the same material but having different thicknesses. Average speed Vfr.mid- this is the value that is obtained when determining the speed at the moment of the first entry.
In similar studies of plexiglass plates, the speed Vfr.mid when changing plate thickness h remains constant, from which we can conclude that in plexiglass (non-resonator plate) the zones Δh are missing.
When emitted by an emitter disk 1 harmonic signal, at the natural frequency of the sounded resonator plate f 0, that is, at resonance, emf. on the destination disk 3 disappears but appears on the destination disc 4 . This effect is called acoustic resonance absorption (ARA).

Rice. 1

Piezoceramic disk emitter 2 , sound plate 1 and piezoceramic receiver disks 3 And 4 are in liquid (water or oil).
Thus, at resonance there is a reorientation of the primary field emitted by the piezoelectric transducer 1 , in the orthogonal direction. The field rotation in the orthogonal direction occurs in the presence of near-surface zones Δ h.
Relationship between the presence of zones Δ h and rotating the field in the orthogonal direction is quite simple. The fact is that the speed of movement of any object or the speed of propagation of any process cannot change without external influence. Therefore, in fact, in the zone Δ h it is not the speed of front propagation that changes V fr, and her x -component, which is possible only if there is an occurrence y -component. In other words, the vector remains constant in magnitude, but in the zones Δ h the vector rotates V fr.
That is, it turns out that when a resonator layer is impacted, its surfaces become emitters of its own frequency f 0, and with a harmonic emitter, the resonator layer becomes sound opaque at resonance. But in both cases, under any influence, a field of elastic vibrations propagates along the resonator layer with a frequency f 0 .
Acoustic isolation of a resonator layer at its natural frequency from adjacent objects has been used for a very long time. Thus, it was noticed that if you put your ear to the ground, you can hear cavalry over enormous distances. In fact, it is not the cavalry that is heard, but the natural vibrations of the rock resonator layer, excited by the horse’s hooves. The very weak attenuation of the field propagating along the resonator layer is precisely a consequence of its acoustic isolation from the adjacent rocks.
When a rock mass is impacted during seismic exploration, the resulting field of elastic vibrations propagates along the rock bedding. This contradicts the fundamentals of seismic exploration, which states that the field resulting from an impact spreads out in all directions.
This is a very serious moment for understanding the operating principle of seismic exploration. It turns out that the signals received on seismograms come not from below, not from the depths, but from the side, since they propagate exclusively ALONG the bedding.
In the spectral analysis of seismic signals, it turned out that relation (1) is satisfied when the coefficient is k in the numerator equal to 2500m/s. In this case, the error in determining the thickness of the rock layer does not exceed 10%.
It must be assumed that a process oriented in the direction y with directed radiation in the direction x , is transverse. And thus, it can be argued that one’s own oscillatory process is formed by transverse waves, and the coefficient k there's nothing more than speed transverse waves Vsh.
The discovery of essentially new, previously unknown oscillatory systems requires a restructuring of thinking. When at one time it was discovered that the Earth is a sphere, then the awareness of this, as well as the transition from geocentric to heliocentric system, demanded a restructuring of the consciousness of the inhabitants of the Earth. However, this restructuring took several centuries, since this new information did not require any special changes in the algorithms of living conditions. Now the situation is somewhat different.
Due to the fact that our planet consists largely of rock layers, it turns out that in general it is a collection of oscillatory systems. This means that any impact on the Earth’s surface should cause a reaction in the form of a set of harmonic damped processes. If the impact is vibrational, then resonance phenomena become possible.
When considering resonant phenomena, there is a need to take into account a parameter characteristic of oscillatory systems - quality factor Q. The very definition of quality factor contains information about the colossal destructive potential of resonance. The quality factor Q shows how many times the vibration amplitude increases in the event of resonance.
Real values ​​of Q for oscillatory systems implemented by geological structures located in the earth's thickness can reach several hundred. And if in the zone of such a high-Q oscillatory system there is an object that has a vibration (dynamic) effect on the ground, then the amplitude of the vibration of this object will increase exactly that many times.
However, the increase in vibration magnitude has certain limitations. These limitations are determined by the fact that at a certain vibration amplitude, elastic deformations are exceeded and destruction occurs. The soil that is exposed to vibration can collapse, and this is manifested by instantaneous, explosive subsidence, with the formation of a crater. When reinforcing the soil with various kinds of reinforced concrete structures (for example, a reinforced concrete dam for a hydroelectric power station), the studs on which the generator is attached to the dam may fail and break.
At small values ​​of Q (say, up to 10), resonance manifests itself as increased vibration. This is unpleasant for the operating personnel; it leads to the formation of various kinds of backlash and imbalance in the operating mechanism, but such a low-Q resonance will not cause crushing, instant destruction.
If Q is significantly greater than the limiting value at which the vibration amplitude causes inevitable destruction, resonance can only exist for a short time. So, let’s say that with the standard vibration frequency of the dynamo 50 Hz, directly under this installation lies a geological structure that has a natural frequency of, say, 25 Hz with a quality factor Q = 200. Then, during the entire period of normal operation, vibration will be within normal limits. However, suppose that for some reason the machine needs to be stopped, and then, during the process of stopping, for some time, its rotation frequency will be close to the resonant one, 25 Hz. In the resonance zone, a smooth increase in the vibration amplitude will begin. And here the question is how quickly the rotor speed passes the resonance zone, and whether the vibration amplitude has time to increase to a destructive value.
It is easy to notice that here, as an example, the situation that developed at the Sayano-Shushenskaya HPP was considered. There, the vibration of hydraulic units in normal operating mode increased to unacceptable values. And when the decision was made to stop, the speed began to decrease very slowly. As a result, when passing through the high-Q resonance zone, the vibration amplitude managed to increase so much that the studs securing the hydraulic unit could not stand it. And, by the way, the recorders of the hydraulic unit showed an increase in vibration by 600 times.
A characteristic sign and harbinger of resonant destruction is an increase in vibration.
The first reliable evidence of the presence of such a precursor occurred during the Chernobyl accident. There, after all, it all started with a change in the reactor mode and, accordingly, the rotation speed of the units. At the same time, vibration began, the amplitude of which began to quickly increase, reaching such a level that people began to leave this area in panic. The vibration was interrupted by a seismic shock (explosive destruction of the soil), noted by seismologists. And only half a minute after this, the destruction of the reactor occurred.
Subsequently, information appeared that this harbinger occurs during the destruction of various types of pumping stations. In the same way, when the vibration frequency of the compressor changes, the vibration amplitude suddenly begins to increase, ending with the equipment sinking into the ground. The cause of such an event is usually cited as either a terrorist attack or poor-quality piles on which the station stands.
Railway accidents often occur when, for no apparent reason, a train breaks into two parts, when suddenly, suddenly, an embankment collapses explosively, forming a depression, and instantly destroyed sleepers and pieces of rails fall into this funnel. It is at this moment of track destruction that the train breaks. However, in the car, which turns out to be the last one to pass through this zone, there is a strong vibration, which ends with the instant destruction of the embankment.
On August 13, 2007, such an accident occurred in the Novgorod region with train N166 Moscow - St. Petersburg. Eyewitnesses later described what happened: “...at first the train began to shake, followed by a bang. The guides, who have been working on this route for many years, later admitted that they began to say goodbye to life, since this was the first time in their memory that this had happened.” The key point is that witnesses felt a strong vibration before the impact.
On March 3, 2009, a six-story archive building suddenly collapsed in Cologne. As reported by Reuters, there was a rumble and strong vibration before the collapse. “The table I was sitting at shook and I thought someone had accidentally kicked it,” said one visitor to the archive. - After everything started to shake like during an earthquake" The house turned into a pile of bricks in just seconds. A police spokesman told reporters that "it looked like an explosion" with bricks, boards and pieces of cement scattered across the pavement in a radius of up to 70 meters. A metro line runs under the archive building, the tunnel of which also collapsed. The source of the vibration, as it turned out, was located in the subway tunnel. This source was a drilling rig operating there.
The physics of resonant damage is discussed in detail in the works. Here it seems necessary to pose the following question. It is well known that an increase in vibration amplitude, ending in an explosion-like destruction, is uniquely associated with resonance phenomena. So why do we never hear the word “resonance” when investigating disasters that had such a precursor? The reason turned out to be purely psychological. According to the established opinion, there are NO oscillatory systems in the earth's thickness. And if there are no oscillatory systems, then there can be no talk of resonance.
If we nevertheless assume the assumption of resonance, then the question of the oscillatory system is inevitable. Because without an oscillatory system there can be no resonance.
Further, if we assume that the earth's strata really represent a set of oscillatory systems, then this undermines the foundations of seismic exploration. After all, consideration of seismic exploration is possible only within the framework of its generally accepted model, according to which the earth's strata is a set of reflecting boundaries.
It doesn't matter whether seismic exploration provides information or not, because it is a colossal, multi-billion dollar business that cannot be touched. A business built on falsifications, but so huge that seismic exploration no longer needs anyone to confirm it.
Now there are probably no functioning scientists who would not know that it is a proven fact that our planet is a collection of oscillatory systems. But now they have main task- pretend that they don’t know this. Any discovery to one degree or another negates the previous level of knowledge. Yes, indeed, if this point of view were mastered and accepted, the number of man-made disasters would decline. But alas, scientists don’t need this. For them, the main thing is to survive until the end of their lives at the level they have achieved, and so that no one crosses out the level of knowledge at which they reached their heights. And this certainly outweighs in importance for them all those catastrophes that could have been prevented.

LITERATURE

1. Glikman A.G. The effect of acoustic resonance absorption (ARA) as the basis of a new paradigm for the field theory of elastic oscillations.
2. Certificate from Northern Express conductors www.newsru.com/russia/14aug2007/train.html
3. Evidence of the destruction of the archive in Cologne www.gazeta.ru/social/2009/03/04/2952320.shtml
4. Glikman A.G. Vibration and resonance phenomena in our lives (what happened at the Sayano-Shushenskaya hydroelectric station)
5. Glikman A.G. Planet Earth as a set of oscillatory systems and man-made and natural earthquakes as consequences of this

under the hooves of a squadron of guards cavalry

The Egyptian bridge across the Fontanka River in St. Petersburg collapses.

Imagine that you are standing on a swinging wooden slatted bridge. It is clear that if you start swaying in time with the swaying of the bridge, the bridge will begin to sway even more.

Real modern bridges also, in fact, oscillate imperceptibly to the naked eye. Architects know that the phenomenon of resonance (that is, the coincidence of the natural frequency with the frequency of external influence) can lead to catastrophic consequences.

Egyptian chain bridge over the Fontanka

So, on February 2, 1905, the Egyptian Bridge in the city of St. Petersburg collapsed when a horse squadron was passing across it. It is believed that the cause of the incident was that the riders, while prancing on their horses, came into resonance with the bridge’s own vibrations.
On school lessons physicists, when studying the phenomenon of resonance, often give an example of this destruction, when a squadron of the Horse Guards Regiment passed “in step” across the bridge in one direction, and 11 sleighs with drivers in the opposite direction.
Typically, a military squad takes 120 steps per minute, and this frequency (2 Hz) coincided with the natural frequency of the structure. With each step, the range of vibrations of the span increased, and finally the bridge could not stand it. The bridge resonated and collapsed. It was one of five suspension bridges in the city.
The entire deck of the bridge, along with the railings and fastenings, broke the chains and broke part of the cast-iron support, broke through the ice and ended up at the bottom of the river.
Fortunately, there were no casualties and everyone managed to get ashore. According to official information, there were no serious injuries.
Subsequently, the military was forbidden to walk across the bridges in lockstep. There was even a special command: “Step at random!”

Egyptian bridge over the Fontanka River. The bridge got its name because of its unique design.

Currently, the sphinxes are all that remains of the first bridge. Now this bridge is neither chain nor suspension.

And in 1940, the Tacoma Bridge in the USA collapsed due to resonant vibrations. The photo shows how it was “twisted”.