RU2756998C1 - Method for destroying material solid body under local highly intensive heat impact on surface thereof - Google Patents

Abstract

FIELD: engineering.

SUBSTANCE: invention relates to the field of destruction of a material solid body (MSB) by at least two sources of local highly intensive heat impact (LHIHI), forming an impact area consisting of figures selected from a group: a circle, an ellipse, an oval, assuming that the maximum concentration coefficient of thermoelastic stresses attributed to the interference of elastic waves in this area is achieved, and is aimed at providing effective modes of LHIHI sources on the surface of the MSB for destruction thereof, including technical apparatuses (TA), by reducing the ultimate tensile strength of the material of the solid body or reducing the load-bearing capacity of the structure of technical apparatuses made of metals, alloys, composite materials, as well as optical and optoelectronic apparatuses. Thermoelastic (thermal) stresses are a type of mechanical stress caused in the MSB by a change in the temperature or the unevenness of distribution thereof. Thermoelastic (thermal) stresses occur in the MSB due to the limited possibility of thermal expansion (compression) from the surrounding parts of the body or from other bodies surrounding the body. Thermoelastic (thermal) stresses can cause destruction of the MSB, parts and structural elements of the TA. LHIHI is understood as the impact of a heat flow source only on a certain (limited) part of the surface of the MSB in the form of a heat spot of various shapes, figures, and sizes.

EFFECT: provided effective modes of LHIHI sources on the surface of the MSB for destruction thereof.

1 cl, 16 dwg

Description

The invention relates to the field of destruction of a material solid, at least by two sources of local high-intensity thermal effect (LVHT), forming an area of influence, consisting of figures selected from the group: circle, ellipse, oval based on the conditions for achieving the maximum concentration coefficient of thermoelastic stresses due to interference waves of elasticity in this area and is aimed at providing effective modes of sources of local high-intensity thermal effects on the surface of a material solid (MTT) for its destruction, including technical devices (TC), by reducing the tensile strength of the solid material, or reducing the bearing capacity design of technical devices made of metals, alloys, composite materials, as well as optical and optoelectronic devices.

Thermoelastic (thermal) stresses are a type of mechanical stress that occurs in a solid material body due to a change in temperature or unevenness of its distribution. In a solid, thermoelastic (thermal) stresses arise from the limitation of the possibility of thermal expansion (contraction) from the side of the surrounding parts of the body or from other bodies surrounding the given body. Thermoelastic (thermal) stresses can cause the destruction of a material solid, parts and structural elements of technical devices. Local heat flux is understood as the effect of a heat flux source only on a certain (limited) part of the surface of the investigated material solid in the form of a heat spot of various shapes and sizes.

Known experimental studies of the behavior of thin-walled cylindrical shells of the TU under the action of operational loads and local high-intensity thermal exposure, set out in the works [1, 2, 3, 4, 5, 6]. The destructive effect is achieved due to the radiant heating of the TC surface by the LVTV source and, as a consequence, the destruction of the TC due to a decrease in the ultimate strength of the material or the bearing capacity of the structure.

Experimental studies were carried out on the experimental installations "Impulse" and "Kipr-1", using optical quantum generators (LQGs). Three sources of pulsed laser radiation with an exposure time τ ~ 1 ms were used on the "Impulse" setup. The pulse energy of each laser source is 1000 J, the wavelength is λ = 1.06 μm.

On the experimental installation "Cyprus-1" used one powerful continuous gas laser, which is shown in Fig. 1. The power of this installation with continuous radiation is 1000 W, wavelength λ = 10.6 microns. The outlet spot diameter is d = 0.041 m. Supplementing this setup with a set of long-focus salt optics with a focal length F = 0.1; 0.2; 0.6; 2; 3; 4 meters allow changing the heat flux density q and the diameter of the local heat spot.

LVTV was carried out on a model of smooth cylindrical shells made of aluminum alloys of the AMG, AMG-2, AVT-1 types.

The construction of such a loading device is shown in FIG. 2. This design provides loading of the inner cavity of the shell with the pressure of compressed gas or liquid and loading the shell with axial compressive force through the pneumatic cylinder. The design of the loading device makes it possible to ensure reliable tightness of the shell with the simultaneous action of operational loads on the shell in the form of internal pressure and the action of axial compressive force, as well as LVTV.

The nature of the destruction of models of a smooth cylindrical shell at various values of the heat flux density q and the parameter P / P _o is shown in Fig. 3.

Where: Р - current pressure value; P _o - limiting static pressure at which the shell collapses; q is the heat flux density; 1 - not collapsed shell; 2 - complete fragmentation destruction; 3 - shell with through cracks (slots); 4 - a shell with holes.

The temperature in the place of local impact reached values of the order of 300… 350 ° С. With an increase in internal pressure (P / P _o = 0.582), brittle fracture is observed with detachment of a part of the surface (hole) along the border of a local heat spot when exposed to a local high-intensity thermal effect (Fig. 4, Fig. 5). In the photograph shown in FIG. 5, it can be seen that the destruction occurred along the contour of the local heat spot. It should be noted that part of the shell (in the form of a lid) did not come off completely along the entire contour of the heat spot, but only partially and due to excess pressure bent to the side, maintaining a single whole with the shell, the so-called "open door" effect or the "not completely open tin can ". A similar nature of shell destruction under a local high-intensity thermal effect can only be explained by the presence of significant thermal (thermoelastic) stresses arising at the boundary of the local heat spot. Additional experiments on models made of glass, as well as other materials that absorb radiation, with a laser wavelength λ = 10.6 μm, confirmed the nature of destruction along the contour of a local heat spot.

If the material of the shell works in the region of ultimate strength (P / Po = 0.678 and higher), complete fragile fragmentation of the shell occurs (Fig. 6).

Fracture with detachment of a part of the surface cannot be explained by the concentration of the maximum circumferential stresses; therefore, it was assumed that significant thermal (thermoelastic) stresses appear at the boundary of the local HPHT spot, which are functions of time [3, 4]. It is the thermal (thermoelastic) stresses that can lead to the destruction of the shell with the separation of a part of the surface.

In order to confirm or refute this assumption, it became necessary to determine the characteristic regularities of the destruction of models of thin-walled cylindrical shells under local thermal action on models made of piezo-optical materials by the method of polarization-optical measurements.

Thermoelastic (thermal) stresses are a type of mechanical stress that occurs in a solid material body due to a change in temperature or unevenness of its distribution. In a solid, thermoelastic (thermal) stresses arise from the limitation of the possibility of thermal expansion (contraction) from the side of the surrounding parts of the body or from other bodies surrounding the given body. Thermoelastic (thermal) stresses can be the cause of the destruction of a material solid, parts and structural elements of technical devices and, accordingly, require studying the picture of the stress-strain state and the danger of thermoelastic stresses arising in a material solid under local thermal action. Local heat flux is understood as the effect of a heat flux source only on a certain (limited) part of the surface of the investigated material solid in the form of a heat spot of various shapes and sizes.

Known, experimental and theoretical studies of the picture of the stress-strain state of structural elements of technical devices under local thermal exposure [3, 4, 8] and the results of experimental studies of the hazard of temperature stresses at the boundary of the heating spot using the coefficient of thermal stress concentration [5]. The basis of the polarization-optical method is the measurement of birefringence. Some isotropic materials, when stresses or strains occur in them, become optically anisotropic like crystals. This phenomenon is called artificial birefringence, and now it is more often called the piezo-optical effect [3, 4, 5, 7, 8, 9, 10]. Materials that exhibit such properties markedly are called optically sensitive or piezo-optical. These materials are often referred to as optically active. In addition to glass, piezo-optical materials include celluloid, plexiglass, phenol-formaldehyde resins, epoxy resins, and many other transparent materials.

It is known, a method of studying the stresses and strains of a solid material by the polarization-optical method on a model made of piezo-optical material when exposed to a local heat flow [9]

The polarization experimental setup "Photoelasticity" is presented in [3, 4, 5, 7, 8, 9, 10] and forms the basis for applied research of the stress-strain state of models made of piezo-optical material under local thermal action. The experimental setup "Photoelasticity" for the study of local thermal effects is shown in Fig. 7 and FIG. 8 and is a flat polariscope, the principle of operation of which is based on the use of the properties of polarized light. Experimental setup "Photoelasticity" includes: 1 - light source, 2 - polarizer, 3 - analyzer, 4 - investigated model, 5 - heating furnace, 6 - heat supply rod, 7 - thermostated chamber for models, 8 - device for loading the model compressive forces, 9 - device for loading the model with tensile forces. The experimental setup includes a number of specially designed systems, which include: a system of plane-polarized light with polaroid plates that convert natural light into plane-polarized light, a system for loading models with axial tensile forces or compressive forces, a system for thermostating samples that provide a given temperature of the model under study , a system of heat supply rods that provide a local high-intensity thermal effect on the model, a system for measuring and recording temperatures in a given interval, a system for monitoring the reliability of recorded temperatures, a system for measuring the intensity of heat flux from heat supply rods by a calorimetric method, a system for photographing models in polarized light. The loading system of the models allows them to be loaded with axial tensile or compressive forces in the range of 0.3 ... 10 KG. A SOUL-type furnace is used as a heater, with a maximum operating temperature of up to 1200 ° C. The provision of local contact heat effect is carried out by copper or brass cylindrical rods (heat supply rods), of various diameters, heated in the working chamber of the SOUL furnace. In experimental studies, rods of various diameters d _c = (10; 15; 20; 24; 28; 44) mm were used. The geometrical dimensions of model disks made of piezo-optical (optically sensitive) material are as follows: disk diameter D = 68 mm; disc thickness d = 12 mm.

Maintaining a given exposure temperature is controlled by varying the voltage applied to the heating elements of the furnace. The sample thermostatting system consists of a chamber, the inner cavity of which is filled with oil; electric heating elements with an automatic switching on and off system in a given temperature range.

The plane-stressed model is, in the general case, optically inhomogeneous in its plane (in the plane of the wave front). Therefore, the image of the model on the screen of the polarization unit will be illuminated unevenly, as a result, the image of the model on the screen of the unit will be covered with a system of two dark and light stripes with smooth transitions (Fig. 9-12). The dark stripes include isoclines and isochromes (stripes).

To analyze the stress-strain state of a model, a fundamental method is used, the isochrom-stripe method [7]. The intensity of light also changes depending on the magnitude of the phase shift and turns out to be equal to zero when Ф = 0 or

where n is a positive number

If the phase shift is 0, 2π, 4π ..., then at these points the light intensity will be zero. With elastic deformation of an initially homogeneous isotropic model, isochromes-stripes determine the locus of points with the same difference in principal stresses. Isochromes-stripes of zero order or points with zero path difference determine the locus of points where the difference in principal stresses is zero.

To detect isotropic points and zero isochromic stripes, the model is shone through with natural, that is, white light, while they look like black spots or black stripes on a colored background.

Isochrome-band is the locus of these points, corresponding to a constant for each band (and different for different bands) value of the optical path difference (δ), equal to

The value n = 1, 2, 3 ..., a positive number, is called the order of the stripe-isochromes and is set by counting the number of darkenings that have passed through the point under study during the loading process of the model or local heat exposure. The order of the band n is directly proportional to the optical path difference δ, nm, and is inversely proportional to the light wavelength λ, nm. In addition, the order of the strip n is proportional to the difference between the principal stresses σ ₁ and σ ₂ , n / m ² , or the doubled maximum shear stresses 2τ _max , n / m ² .

When determining the price of isochromes-stripes, the difference between the principal stresses in the elastic isotropic model is expressed through the order of isochromes-stripes.

attitude

is called the price of a strip of material, then

The resulting relationship is called Wertheim's law [7]. Material strip price (or optical constant) σ _1.0 , n / m. In the GHS system, it is usually measured in kg / cm per lane. The price of a strip of material is the difference between the principal stresses that cause the appearance of one strip in a model with a thickness of d = 1 cm. The value of the price of a strip of material is determined by calibration tests. The value of σ _d is determined by the relation

and is called the price of the pattern strip. It's obvious that

The results of experimental studies of the local thermal effect on plane models made of piezo-optical material are well illustrated by photographs of a qualitative picture of isoclines and isochromic bands arising in models of the stress-strain state. The photograph (Fig. 9-12) shows the interference patterns of isoclines and isochromic bands in a model subjected to local thermal action.

In the center of the model, there is a crossing of two dark lines, which are isoclines. This indicates that the thermal effect was carried out axisymmetrically, with a uniform temperature distribution over the diameter of the local heat spot.

The diameter of the heat supply rod for the model shown in FIG. 9 corresponds to d _c = 28 mm.

For the investigated models (Fig. 10; Fig. 11; Fig. 12) the diameters of the heat supply rods were respectively d _c = (44; 24; 20) mm. These photographs show qualitative pictures of isoclines and isochromic bands arising in models under the action of a local heat flux from a round heat supply rod. In the center of the models, dark) (shaped stripes (isoclines) are visible, which cannot be fully compensated for by synchronous rotation of the polarizer and analyzer.

On all models, the boundary of the local thermal effect is clearly visible, which corresponds to the diameter of the heat supply rod. The dark stripes, which are regular concentric circles, are isochromic stripes, i.e. locus of points with the same principal stress difference. Moreover, the smaller the distance between these concentric circles, the greater the gradient of the difference between the principal stresses. The smallest distance between the stripes is located just at the boundary of the local thermal effect, which indicates a significant concentration of the arising thermoelastic (thermal) stresses in this particular zone, which is only from -0.5 to +3.0 mm along the radius of the model.

Known, the closest in technical essence, a method for studying thermal stresses arising in a solid material by the polarization-optical method on a model made of piezo-optical material when exposed to a local heat flux, with the definition of the theoretical coefficient of thermal stress concentration [10].

This decision was made as a prototype.

The main disadvantages of this method, taken as a prototype [10], is that to create a local heat flux, only one source of local heat effect is used, which forms at the border of a local heat spot in the region from -0.5 to +3.0 mm from its edge maximum thermal (thermoelastic) stresses.

The aim of the invention is to develop a method for the destruction of a material solid body with LHTV on its surface, at least two LHTV sources and is aimed at providing effective modes of LHHT sources on the surface of a material solid for its destruction, including technical devices made of metals, alloys, composite materials, as well as optical and optoelectronic devices.

This goal is achieved by using at least two sources of LVTV, forming on the surface of a material solid body an area of influence, consisting of figures selected from the group: circle, ellipse, oval, based on the conditions for achieving the maximum coefficient of concentration of thermoelastic stresses caused by wave interference elasticity in this area.

To achieve this goal, an experimental study was carried out of the field of thermal (thermoelastic) stresses arising in the models under the local thermal effect of the heat source shown in Fig. 9-12. For this purpose, an MP-7 polarizing microscope was used. Initially, the number of isochromic stripes was determined at each selected point of the field along the radius of the model. The zero point was taken to be the boundary of the local thermal effect, which coincided with the diameter of the impact spot and is equal to the diameter of the round heat supply rod. This border is clearly visible on the models. Then, with a step S = 1 mm along the radius of the model, the number of isochromic bands was determined. According to the measurement results, graphical dependences of the change in the number of isochromic bands N along the radius of the R model were plotted (Fig. 13). In the presented graphical dependencies (Fig. 13), at the border of the local thermal effect, the number of isochromic bands increases sharply and reaches the maximum value N = 24 ... 25 at a distance from -0.5 to +3.0 mm from the spot border, where N is the number isochrome stripes, positive number, R - model radius, mm.

The zero isochrome-band was determined, and then, with a step S = 1 mm along the radius of the model, the number of isochrome-bands and their order were determined. An accurate measurement of the order of isochromic bands at the point under consideration on the contour was carried out by the compensation method using an MP-7 polarizing microscope. Based on the measurement results, graphical dependences of the change in the order of the isochromes-band n along the radius of the R model were plotted (Fig. 14). On the presented graphical dependencies (Fig. 14) at the border of the local thermal effect, the order of the isochromes-band increases sharply and reaches the maximum value n = 2.95 ... 3.25 at a distance from -0.5 to +3.0 mm from the border of the local thermal spots, and then begins to decrease, tending to the nominal value. The isocline and isochromic interference patterns are shown in FIG. 10 for model 1 in FIG. 9 for model 2.

The order of the strip n is directly proportional to the difference between the principal stresses (σ ₁ -σ ₂ ) arising in the model under local thermal impact or the highest shear stresses 2τ _max , i.e.:

where K is the coefficient of the optical constant, determined by formulas (3, 4), using special calibration models [7].

Graphical dependences of changes in the difference between the principal stresses (σ ₁ -σ ₂ ) or the highest shear stresses 2τ _max along the radius of the model will be similar to the graph (Fig. 14) of the change in the order of the isochromes-band n along the radius of the model.

To determine the theoretical concentration factor of thermal (thermoelastic) stresses, it is not necessary to know the maximum and nominal stresses. When determining the theoretical coefficient of concentration of thermal (thermoelastic) stresses in this case, it is possible not to know the optical constant of the material and the magnitude of the applied load, but to measure the order of isochromic bands, taken as nominal.

where K _t is the theoretical concentration coefficient of thermal (thermoelastic) stresses arising at the boundary of the heat spot, under local thermal action on an unloaded model made of piezo-optical material, is directly proportional to the maximum order of the strip (n _max ) and inversely proportional to the nominal order of the strip (n _nom ). The theoretical coefficient of concentration of thermal (thermoelastic) stresses is a dimensionless quantity. The maximum order of the strip (n _max ) is taken to be the largest order of the strip at the place of concentration of thermal (thermoelastic) stresses at the boundary of the local heat spot, and the nominal order of the strip (n _nom ) is taken to be the order of the strip, which is determined in the section with a uniform uniaxial stress distribution or on a section remote from the boundary of the local heat spot at a distance equal to from 1 to 3 radii of the local heat spot (R _p ).

The order of the band is determined by the graphical dependencies (Fig. 14), or you can use the exact measurement of the order of the bands at the point under consideration on the contour by the compensation method. The interference pattern of the arising thermal (thermoelastic) stresses under the action of a local heat flux on the piezo-optical model is investigated and the theoretical coefficient of the concentration of thermal (thermoelastic) stresses arising in the model from a piezo-optical material under local thermal action is determined, in this case it will be K _t = 2.95 ... 3.25.

The interference pattern of the arising thermal (thermoelastic) stresses under the action of a local heat flux on the piezo-optical model is investigated.

Analyzing the resulting interference pattern of isoclines and isochromic bands under local thermal exposure, a number of important conclusions can be drawn:

First, the presence of significant thermal (thermoelastic) stresses arising in the initially unloaded isotropic homogeneous model at the boundary of the spot of local thermal action was established, which is confirmed by the maximum number of isochromic bands (N) and the maximum order of the strip (n) in the zone from -0.5 to + 3.0 mm from the edge of the local heat spot.

Second, the occurrence of thermal (thermoelastic) stresses does not depend on the diameter and shape of the spot of the local thermal effect, but they arise only at the boundary of the local heat spot in the zone from -0.5 to +3.0 mm from its edge.

Third, in unloaded models in the hottest local heat spot, there are practically no thermal (thermoelastic) stresses.

Fourth, the resulting acting and residual thermal (thermoelastic) stresses under local thermal action correspond to the compression stress.

Fifth, the danger of thermal (thermoelastic) stresses can be taken into account through the theoretical coefficient of concentration of thermal (thermoelastic) stresses K _t = 2.95 ... 3.25.

Sixth, with a real local high-intensity thermal effect on a material solid, the most dangerous place is the boundary of the spot of local thermal effect, and it is in this place that the real structure is destroyed.

Seventh - acting and residual thermal (thermoelastic) stresses at the boundary of a local heat spot lead to a decrease in the ultimate strength of a solid material or a decrease in the bearing capacity of the structure of a technical device, which leads to their destruction.

The aim of the invention is to develop a method for the destruction of a material solid body with LHTV on its surface, at least two LHTV sources and is aimed at providing effective modes of LHHT sources on the surface of a material solid for its destruction, including technical devices made of metals, alloys, composite materials, as well as optical and optoelectronic devices.

This goal is achieved by forming an area of influence, consisting of figures selected from the group: circle, oval, ellipse, based on the conditions for achieving the maximum concentration coefficient of thermoelastic stresses caused by the interference of elastic waves in this area.

FIG. 15a shows a variant of the formation of the area of influence using two sources of LVTV, which form a local heat spot on the surface of the MTT in the form of two round figures with the formation of conditions for achieving the maximum coefficient of concentration of thermoelastic stresses caused by the interference of elastic waves in this area.

FIG. 15b shows a variant of the formation of the area of influence using two sources of LVTV, forming on the surface of the MTT a local heat spot in the form of two ellipses or two oval figures with the formation of conditions for achieving the maximum coefficient of concentration of thermoelastic stresses caused by the interference of elastic waves in this area.

FIG. 16a shows a variant of the formation of the area of influence using three sources of LVTV, forming on the surface of the MTT a local heat spot in the form of three round figures with the formation of conditions for achieving the maximum coefficient of concentration of thermoelastic stresses caused by the interference of elastic waves in this area.

FIG. 16b shows a variant of the formation of the area of influence using three sources of LVTV, forming on the surface of the MTT a local heat spot in the form of three ellipses or three oval figures with the formation of conditions for achieving the maximum concentration coefficient of thermoelastic stresses caused by the interference of elastic waves in this area.

Where:

1 - a local heat spot on the surface of a material solid at a local high-intensity thermal effect;

2 - the region of maximum thermoelastic stresses or the region of achieving the maximum coefficient of concentration of thermoelastic stresses.

The purpose of the invention has been achieved, the use of the described method makes it possible to destroy a material solid under a local high-intensity thermal effect on its surface using at least two sources of high-voltage heat-resistant materials, which form the region of thermoelastic stresses based on the conditions for achieving the maximum coefficient of concentration of thermoelastic stresses caused by the interference of elastic waves in this area.

Literature:

1. Esaulov S.K. Research report. Investigation of the resistance of materials and structural elements of technical devices to thermal effects, Ministry of Defense of the USSR, Riga, 1990, 158 p.

2. Kostoglotov AI, Baskakov VN, Krasnov AA, Yunak YI, Behavior of thin-walled cylindrical shells at local thermal shock. Kiev, Nauk. dumka, Problems of Strength, 1987, no. 7, p. 71-73.

3. Esaulov S.K., Kukushkin S.S. Article. System experimental-theoretical studies of the behavior of thin-walled cylindrical shells under the action of operational loads and local action of high-intensity heat sources, Ministry of Defense of the Russian Federation, Proceedings of the Central Research Institute of the Ministry of Defense of the Russian Federation, No. 112, 2013, p. 11-19.

4. Esaulov S.K., Kukushkin S.S. Article. Experimental and theoretical studies of the picture of the stress-strain state of structural elements of technical devices under local thermal impact, Ministry of Defense of the Russian Federation, Proceedings of the 4 Central Research Institute of the Ministry of Defense of the Russian Federation, No. 112, 2013, p. 27-34.

5. Esaulov S.K., Kukushkin S.S. Article. Results of experimental studies of the hazard of temperature stresses at the boundary of the heating spot using the coefficient of thermal stress concentration, Ministry of Defense of the Russian Federation, Proceedings of the Central Research Institute of the Ministry of Defense of the Russian Federation, No. 112, 2013, p. 35-43.

6. Esaulov S.K., Zakharov N.S. Research report. B-1 / VIKor, JSC VIKor, 2013, 147 p.

7. A.Ya. Alexandrov, M.Kh. Akhmetzyanov. Polarization-optical methods of deformable body mechanics. M., "Science", 1973, p. 72-73, 80-93, 106-112, 128-144, 217, 234-238, 362-365, 483-487.

8. Esaulov S.K., Kukushkin S.S., Dyundikov E.T., Chepelev A.V., Belov A.N., Trifonova M.A. Article, Experimental studies of the picture of the stress-strain state and the field of thermal stresses arising in structural elements and materials of technical devices under local thermal action on models made of piezo-optical material. Dual technologies, Publishing and Printing Center of CJSC "PSTM", 2016, No. 2, p. 70-76.

9. Esaulov S.K. (RU). Patent for invention RU No. 2610219, 08.02.2017. A method for studying the stresses and strains of a solid material by the polarization-optical method on a model made of a piezo-optical material when exposed to a local heat flux, 1 n. and 23 p.p. formulas.

10. Esaulov S.K. (RU). Patent for invention RU No. 2621458, 06.06.2017. A method for studying thermal stresses arising in a solid material by the polarization-optical method on a model made of piezo-optical material when exposed to a local heat flux, with the determination of the theoretical coefficient of thermal stress concentration, 1 n. and 34 p.p. formulas.

Claims (1)

A method of destruction of a material solid body with a local high-intensity thermal effect on its surface, characterized in that at least two sources of local high-intensity thermal effect are used, forming an area of influence, consisting of figures selected from the group: circle, ellipse, oval, based on the conditions for achieving the maximum concentration coefficient of thermoelastic stresses caused by the interference of elastic waves in this area.

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