System and method for measuring frequency dispersion and attenuation characteristics of elastic waves of rock

Abstract

The invention discloses a system and method for measuring the frequency dispersion and attenuation characteristics of elastic waves of rock, and the system comprises an axial pressure control chamber, the lower part of the axial pressure control chamber is provided with a confining pressure chamber, the pressure applying end of the axial pressure control chamber is located at the upper part of the confining pressure chamber, the interior of the confining pressure chamber is also provided with a probe body, and the probe body is used for bonding with a rock core sample. A positioning and sealing device for placing a rock core sample is also arranged in the confining pressure bin; a heating sheet is further mounted on the inner wall of the confining pressure bin; the positioning and sealing device is also connected with a vibration exciter through a vibration excitation pipeline; the excitation pipeline is provided with a force sensor; the ultrasonic signal generating device is pre-embedded in the probe body, so that the problem that the ultrasonic frequency band test cannot be repeatedly carried out on a sample subjected to the medium-frequency and low-frequency band test is solved, the axial pressure controller and the confining pressure controller adopt a closed-loop control servo hydraulic loading mode to replace a traditional gas pressurization mode, the target pressure can be quickly and accurately achieved, and the test efficiency is improved. And the safety of the experiment process can be ensured under the condition of high confining pressure.

Description

Technical Field

[0001] The present invention relates to a measuring instrument for rock elastic wave dispersion and attenuation characteristics under medium and low frequency conditions. More specifically, the present invention mainly relates to a measuring system and method for rock elastic wave dispersion and attenuation characteristics. Background Art

[0002] In geophysical exploration, the methods for obtaining elastic wave dispersion and attenuation characteristics mainly include seismic exploration, acoustic logging and laboratory measurement. First, traditional laboratory velocity measurements are usually performed in the MHz frequency range, while acoustic logging is performed in the 10KHz frequency range and ground seismic is performed in the 0-100Hz frequency range. There are significant differences in the measurement frequency between different methods. Today, challenging exploration work requires the comprehensive use of all types of data for quantitative interpretation. However, the dispersion of velocity in different frequency ranges makes data integration difficult. The cross-band test procedure for rock elastic wave dispersion and attenuation characteristics is divided into two parts: ultrasonic frequency band and medium and low frequency bands. However, the medium and low frequency test requires aluminum probes to be attached to both ends of the sample and the sample to be sealed with glue, which makes it impossible to test the low-frequency test sample in the ultrasonic frequency band again, hindering repeated experiments. At the same time, the existing medium and low frequency test instruments have the following problems: (1) The medium and low frequency tests are mostly analyzed by stress-strain method. The strain signal of this method is very weak, usually only a few microstrains. No system can completely avoid noise. Even with repeated measurements, effective signals may be drowned out by strong background noise. (2) The use of gas media for pressurization makes the operating environment dangerous and cannot stably simulate the stress environment of rocks. (3) The degree of automation is low, and some are completely manually operated. Summary of the invention

[0003] One of the purposes of the present invention is to address the above-mentioned shortcomings and provide a system and method for measuring the dispersion and attenuation characteristics of rock elastic waves, in order to solve the technical problems in the prior art that similar testing methods have weak strain signals and that medium and low frequency test samples cannot be repeatedly tested in the ultrasonic frequency band.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0005] The present invention provides a measurement system for rock elastic wave dispersion and attenuation characteristics, the measurement system comprising an axial pressure control chamber, a confining pressure chamber is provided at the lower part of the axial pressure control chamber, the pressure-applying end of the axial pressure control chamber is located at the upper part of the confining pressure chamber, a probe body is provided inside the confining pressure chamber, the probe body is used to bond with the core sample, a positioning sealing device is provided inside the confining pressure chamber for placing the core sample, the positioning sealing device corresponds to the pressure-applying end of the axial pressure control chamber; a heating plate is also installed on the inner wall of the confining pressure chamber; the positioning sealing device is also connected to the exciter through an excitation pipeline; a force sensor is installed on the excitation pipeline; the confining pressure chamber is connected to the pore pressure loader through the pore pressure pipeline, the confining pressure chamber is also connected to the pressure relief pipeline, and a pressure relief valve is installed on the pressure relief pipeline; the pressure-applying end of the pore pressure pipeline is used The inner hole is connected to the core sample; a pressure relief sensor is installed on the pressure relief pipe; the confining pressure chamber is connected to the confining pressure loader through the confining pressure pipe, and the axial pressure control room is connected to the axial pressure loader through the axial pressure pipe; a pore pressure sensor is installed on the pore pressure pipe, a confining pressure sensor is installed on the confining pressure pipe, and an axial pressure sensor is installed on the axial pressure pipe; a strain gauge is adhered to the probe body, and the strain gauge is also used to adhere to the core sample. The strain gauge is connected to a data acquisition box through a serial interface, and the data acquisition box and the force sensor, pressure relief sensor, pore pressure sensor, confining pressure sensor, and axial pressure sensor are respectively connected to a computer; the computer is also connected to a function generator, and the function generator is connected to the exciter through a signal amplifier; an ultrasonic signal generating device is also integrated inside the probe body.

[0006] Preferably, a further technical solution is: the vibrator is placed below the positioning and sealing device.

[0007] A further technical solution is: the bore pressure loader includes a cylinder body, a piston is installed in the cylinder body, the piston is connected to a stepper motor through a coupling, the stepper motor is also connected to a speed controller, the stepper motor and the speed controller are connected to the computer, and the pressurized medium in the bore pressure pipeline is silicone oil; the confining pressure loader and the axial pressure sensor have the same structure as the bore pressure loader.

[0008] A further technical solution is: the data acquisition box has a central controller, the central controller is connected to a memory and an A / D converter, the A / D converter is connected to the strain gauge, and the central controller is connected to the computer.

[0009] A further technical solution is that the core sample is wrapped by a potting glue.

[0010] A further technical solution is that the ultrasonic signal generating device is made of piezoelectric ceramics.

[0011] The present invention also provides a method for measuring the dispersion and attenuation characteristics of rock elastic waves. The method uses the above-mentioned measurement system and comprises the following steps:

[0012] Step A: placing the core sample with elastic wave dispersion and attenuation in a positioning and sealing device.

[0013] Step B: Then install the confining pressure chamber, and start the pore pressure loader, the confining pressure loader, and the axial pressure loader to apply pore pressure, confining pressure, and axial pressure to the core sample in the positioning sealing device, respectively.

[0014] Step C: start the ultrasonic signal generating device and the exciter in the probe body, so as to excite the high frequency signal and the medium and low frequency signals to be applied to the core sample.

[0015] Step D: The computer collects data of the core sample through the force sensor, the pressure relief sensor, the pore pressure sensor, the confining pressure sensor, and the axial pressure sensor.

[0016] Step E: The data acquisition box collects real-time stress signals of multiple strain gauges and transmits them to a computer. The computer obtains the energy spectrum of the earthquake source by performing a cross-correlation interference algorithm on two signals in the frequency domain.

[0017] The attenuation characteristic curve is calculated by data acquisition and the phase difference between the continuous signals of the same frequency at any two positions in the core sample.

[0018] A further technical solution is: the core sample is in the shape of a rectangle or a cylinder, and the strain gauges are adhered to its surface at the same distance.

[0019] Compared with the prior art, one of the beneficial effects of the present invention is that by pre-embedding the ultrasonic signal generating device in the probe body, the problem that the samples undergoing medium and low frequency band tests cannot be repeatedly subjected to ultrasonic frequency band tests is solved, and the axial pressure controller and the confining pressure controller adopt a closed-loop controlled servo hydraulic loading method to replace the traditional gas pressurization method, which can quickly and accurately reach the target pressure, and can ensure the safety of the experimental process under high confining pressure. At the same time, a more stable internal temperature field can be obtained after the pressurized medium is changed from gas to silicone oil. At the same time, the interference method is introduced into the processing of medium and low frequency band signals. By performing interference method processing on the strain signals of specific arrangements in the medium and low frequency band samples, the collected signals are more accurate and stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 The figure is a schematic diagram of the structure of a measurement system for illustrating an embodiment of the present invention.

[0021] Figure 2 It is a schematic diagram of the core sample structure for illustrating an embodiment of the present invention.

[0022] Figure 3 It is a schematic diagram for explaining the end surface structure of a probe body in one embodiment of the present invention.

[0023] Figure 4 The figure is used to illustrate the variation of the measured data speed curve with frequency in one embodiment of the present invention.

[0024] Figure 5 The attenuation curve of the measured data varies with frequency in one embodiment of the present invention.

[0025] In the figure, 1 is the confining pressure pipeline, 2 is the axial pressure control room, 3 is the confining pressure chamber, 4 is the heating plate, 5 is the core sample, 6 is the probe body, 7 is the positioning sealing device, 8 is the communication serial port, 9 is the excitation pipeline, 10 is the pressure relief pipeline, 11 is the force sensor, 12 is the exciter, 13 is the pore pressure loader, 14 is the axial pressure loader, 15 is the confining pressure loader, 16 is the data acquisition box, 17 is the pressure relief sensor, 18 is the pressure relief valve, 19 is the confining pressure sensor, 20 is the axial pressure sensor, 21 is the pore pressure sensor, 22 is the function generator, 23 is the signal amplifier, 24 is the pore pressure pipeline, a is the aluminum block, b is the reserved pipeline, c is the piezoelectric ceramic, d is the potting glue, and e is the strain gauge. DETAILED DESCRIPTION

[0026] The present invention will be further described below in conjunction with the accompanying drawings.

[0027] refer to Figure 1 As shown, the rock elastic wave dispersion and attenuation characteristic measurement system in the embodiment of the present invention includes a computer, a sample module, a vibration module, a data acquisition and processing module, a heating module, a pore pressure loading module and a pressure loading module.

[0028] The sample module includes a core sample 5, an aluminum probe 6, and a potting glue wrapped around the sample. The top and bottom of the core sample 5 are connected to the aluminum probe 6 through special quick-drying glue and placed in a positioning sealing device 7.

[0029] The vibration module includes a low-frequency signal generator and an ultrasonic signal generator. The low-frequency signal generator includes a function generator 22, a signal amplifier 23, an exciter 12 and a force sensor 11. The function generator 22, the signal amplifier 23 and the exciter 12 are connected in sequence through a serial interface. The exciter 12 is located at the bottom of the positioning and sealing device 7 and is rigidly connected through the force sensor 11. The ultrasonic signal generator is composed of piezoelectric ceramics and is integrally formed inside the aluminum probe 6, such as Figure 3 shown.

[0030] The above-mentioned pressure loading module includes a confining pressure loading system, an axial pressure loading system and a hole pressure loading system; wherein the confining pressure loading system includes a confining pressure loader 15, and a starting stepper motor, a speed controller, a driving coupling and a piston connected in sequence, and the piston is installed in a silicone oil cylinder. The confining pressure loader 15 is connected to the confining pressure pipeline 1, and drives the ball screw through the motor and the speed controller, thereby pushing the cylinder piston to output the pressure medium (silicone oil) into the confining pressure chamber 3 and output the pressure load. The pressure output range of the confining pressure controller is 0 to 80 MPa, and its pressure resistance range is -20 to 100 MPa.

[0031] Similarly, the above-mentioned axial pressure loading system includes an axial pressure loader 14, and a starting stepper motor, a speed controller, a driving coupling and a piston connected in sequence, and the piston is installed in a silicone oil cylinder. The axial pressure loader 14 is connected to the axial pressure control chamber 2. The axial pressure loader 14 drives the ball screw through the motor and the speed controller, thereby pushing the cylinder piston to output the pressure medium (silicone oil) into the axial pressure control chamber 2 and output the pressure load. The pressure output range of the axial pressure controller is 0 to 6MPa, and its pressure resistance range is -10 to 10MPa.

[0032] The pore pressure loading system includes a pore pressure loader 13 and a pore pressure control pipeline, which is divided into a pore pressure pipeline 24, a pressure relief pipeline 10 and a pressure relief valve 18. The pore pressure loading system generates pressure through the pore pressure loader 13. At the beginning of the test, the pressure is sequentially loaded into the sample through the pore pressure pipeline 24, the core sample 5 and the pressure relief pipeline 10. After the test, the pressure relief valve 18 is opened to unload the pressure; the pressure output range of the pore pressure loader 13 is 0 to 20 MPa, and its pressure resistance range is -10 to 30 MPa.

[0033] The heating module is composed of a heating plate 4 in the confining pressure chamber 3, and the temperature control range is 5 to 70°C.

[0034] The data acquisition and processing module includes strain gauges on the sample and the aluminum block, a data acquisition box 16, a serial interface 8, an axial pressure sensor 20, a confining pressure sensor 19, a pore pressure sensor 21 and a pressure relief sensor 17. The strain gauges are attached to the aluminum probe 6 and the core sample 5 at specific positions using quick-drying glue, such as Figure 2 and Figure 3 As shown, the strain gauge is connected to the data acquisition box 16 through the communication serial port 8 to collect the real-time strain information of the core sample 5, and the collected strain information is transmitted to the computer in real time through the communication serial port 8; the aforementioned axial pressure sensor 20, confining pressure sensor 19, pore pressure inlet sensor 21 and pore pressure outlet sensor 17 are connected to the computer to record the real-time stress information of the core sample. At the same time, the data acquisition box 16 includes a central controller, a memory 8-channel 16-bit A / D converter, and the central controller also terminates the computer.

[0035] The specific processing process of the above data acquisition and processing module is as follows, that is, in another embodiment of the present invention, the core needs to be made into Figure 2 The test sample shown in the figure is a core sample 5 placed in a positioning sealing device 7 and Figure 1 After the equipment is assembled, the pressure relief valve 18 is closed, and the test device is initialized accordingly. According to the test requirements, the heating plate 4, the confining pressure loader 15, the axial pressure loader 14 and the pore pressure loader 13 are started, and the temperature, confining pressure, axial pressure and pore pressure preset in the test plan are input into the computer.

[0036] Specifically, another embodiment of the present invention is a method for measuring rock elastic wave dispersion and attenuation characteristics, which uses the above-mentioned measurement system and is operated according to the following steps:

[0037] Step 1: Place the core sample with elastic wave dispersion and attenuation in a positioning and sealing device. The core sample is in the shape of a rectangle or a cylinder. Figure 2 As shown, the strain gauges are adhered on the surface at the same distance.

[0038] Step 2: Then install the confining pressure chamber, and start the pore pressure loader, confining pressure loader, and axial pressure loader to apply pore pressure, confining pressure, and axial pressure to the core sample in the positioning sealing device, respectively.

[0039] Step 3: Start the ultrasonic signal generating device and the exciter in the probe body, so as to excite the high-frequency signal and the medium-frequency and low-frequency signals to be applied to the core sample.

[0040] Step 4: The computer collects data of the core sample through the force sensor, the pressure relief sensor, the pore pressure sensor, the confining pressure sensor, and the axial pressure sensor.

[0041] Step 5: The data acquisition box collects real-time stress signals from multiple strain gauges and transmits them to a computer. The computer then performs a cross-correlation interference algorithm on two signals in the frequency domain to obtain the energy spectrum of the earthquake source.

[0042] The energy spectrum of the above earthquake source contains dispersion curve and attenuation curve, which are calculated as follows:

[0043] Dispersion curve calculation. A high signal-to-noise ratio system signal can be obtained by interference processing. When the medium and low frequency signals and the ultrasonic signal are excited by the piezoelectric ceramics in the vibrator 12 and the aluminum probe body 6 respectively, the computer receives the data collected by the data acquisition box 16 at any two positions r in the core sample 5. A and r B The real-time stress-strain signal of the strain gauge at is u(r i , s, ω), (i = A, B), by performing r A Place and r BThe energy spectrum of the earthquake source can be obtained by cross-correlation interferometry of the signal at , as shown in formula (1).

[0044] C AB (ω)=u(r A , S,ω)*u(r A ,S,ω) (1)

[0045] where c AB (ω) is the energy spectrum of the earthquake source, ω is the angular frequency; u(r A , s, ω) and are respectively collected by the computer through the acquisition box 16 A and r B Strain signals at two locations; r A and r B are the positions of any two strain gauges; s is the location of the earthquake source. This embodiment uses Tau-p transformation to decompose the data of formula (1) into elastic waves, calculates the frequency-velocity spectrum to reflect the phase velocity of elastic waves with different frequency components, and thus extracts the elastic wave dispersion curve. The process is expressed as:

[0046]

[0047] Where t = τ + px, d(t, x) is the spatiotemporal data, t is time, x is r A Place and r B The distance The integral of the spatial and temporal data d(t, x) is: the upper and lower limits of the integral are -∞ to +∞, respectively. τ and p are the intercept and slope of the tilted stacking. The Tau-p spectrum obtained by the transformation is transformed into the frequency domain and interpolated to obtain the frequency velocity spectrum for dispersion analysis. Figure 4 shown.

[0048] Attenuation curve calculation. When the medium and low frequency signals and the ultrasonic signal are respectively excited by the vibrator 12 and the piezoelectric ceramic in the aluminum probe body 6 to vibrate the vibration module s, the computer receives the continuous signals x(t) and y(t) of the same frequency at any two positions in the sample 5 collected by the data acquisition box 16, and the following expression is obtained:

[0049]

[0050] α0=2πf0 (5)

[0051] Where x(t) and y(t) represent the strain at any two positions at time t; A and B are the amplitudes of signals x(t) and y(t), respectively; α0 is the angular frequency, and are the initial phases at x and y, respectively. Performing cross-correlation operation on x(t) and y(t), we get:

[0052]

[0053] Where R xy (τ) represents the cross-correlation value of signals x(t) and y(t) at a time delay of τ; T is the period of the strain signal; Represents the upper and lower limits of integration, from 0 to T; x(t) is the function of the first signal changing with time t; y(t+τ) is the function of the second signal changing with time t plus the time delay τ; dt is the integral variable representing integration over time t.

[0054] When τ=0

[0055]

[0056] After integration, one of the items is eliminated, that is The relationship between x(t) and y(t) is as follows:

[0057]

[0058] The phase difference is obtained as follows:

[0059]

[0060] The attenuation curve can be obtained based on the phase difference. Figure 5 As shown, the process is expressed as:

[0061]

[0062] Based on the above embodiments of the present invention, it can be seen that the present invention has the following characteristics:

[0063] 1. Pre-embed piezoelectric ceramics in the aluminum block to solve the problem that samples undergoing medium and low frequency tests cannot be repeatedly tested in the ultrasonic frequency band.

[0064] 2. Introduce the interference method into the processing of mid- and low-frequency signals. By using the interference method to process the strain signals of the specific arrangement of the mid- and low-frequency samples, the collected signals are more accurate and stable.

[0065] 3. The axial pressure controller and the confining pressure controller use a closed-loop controlled servo hydraulic loading method to replace the traditional gas pressurization method, which can quickly and accurately reach the target pressure and ensure the safety of the experimental process under high confining pressure. At the same time, a more stable internal temperature field can be obtained after the pressurization medium is changed from gas to silicone oil.

[0066] 4. The computer is used to control the axial pressure controller and the confining pressure controller, and to process and save the data in real time, which significantly improves the automation level of the measurement system.

[0067] In addition to the above, it should be noted that "one embodiment", "another embodiment", "embodiment", etc. mentioned in this specification refer to the specific features, structures or characteristics described in conjunction with the embodiment included in at least one embodiment generally described in this application. The same expression appearing in multiple places in the specification does not necessarily refer to the same embodiment. Further, when describing a specific feature, structure or characteristic in conjunction with any embodiment, it is claimed that the realization of such feature, structure or characteristic in conjunction with other embodiments also falls within the scope of the present invention.

[0068] Although the present invention is described herein with reference to a number of illustrative embodiments of the present invention, it will be appreciated that those skilled in the art may devise many other modifications and implementations that fall within the scope and spirit of the principles disclosed herein. More specifically, within the scope of the present disclosure, drawings, and claims, a variety of variations and improvements may be made to the components and / or layout of the subject combination layout. In addition to variations and improvements made to the components and / or layout, other uses will also be apparent to those skilled in the art.

Claims

1. A system for measuring the dispersion and attenuation characteristics of rock elastic waves, characterized by: The measurement system comprises an axial pressure control chamber (2), a confining pressure chamber (3) is provided at the lower part of the axial pressure control chamber (2), a pressure-applying end of the axial pressure control chamber (2) is located at the upper part of the confining pressure chamber (3), a probe body (6) is provided inside the confining pressure chamber (3), the probe body (6) is used to bond with a core sample (5), a positioning sealing device (7) for placing the core sample (5) is provided inside the confining pressure chamber (3), and the positioning sealing device (7) corresponds to the pressure-applying end of the axial pressure control chamber (2); a heating plate (4) is also installed on the inner wall of the confining pressure chamber (3); The positioning sealing device (7) is also connected to the vibrator (12) via a vibrating pipe (9); the vibrating pipe (9) is equipped with a force sensor (11); The confining pressure chamber (3) is connected to the pore pressure loader (13) through the pore pressure pipeline (24), and the confining pressure chamber (3) is also connected to the pressure relief pipeline (10), and a pressure relief valve (18) is installed on the pressure relief pipeline (10); the pressure-applying end of the pore pressure pipeline (24) is used to communicate with the inner hole of the core sample (5); and a pressure relief sensor (17) is installed on the pressure relief pipeline (10); The confining pressure chamber (3) is connected to the confining pressure loader (15) through the confining pressure pipeline (1), and the axial pressure control chamber (2) is connected to the axial pressure loader (14) through the axial pressure pipeline; The bore pressure pipe (24) is provided with a bore pressure sensor (21), the confining pressure pipe (1) is provided with a confining pressure sensor (19), and the axial pressure pipe is provided with an axial pressure sensor (20); The probe body (6) is adhered with a strain gauge, and the strain gauge is also used to adhere to the core sample (5). The strain gauge is connected to the data acquisition box (16) through a serial interface. The data acquisition box (16) and the force sensor (11), the pressure relief sensor (17), the pore pressure sensor (21), the confining pressure sensor (19), and the axial pressure sensor (20) are respectively connected to a computer; The computer is also connected to a function generator (22), and the function generator (22) is connected to the exciter (12) via a signal amplifier (23); an ultrasonic signal generating device is also integrated inside the probe body (6).

2. The rock elastic wave dispersion and attenuation characteristics measurement system according to claim 1 is characterized by: The vibration exciter (12) is placed below the positioning and sealing device (7).

3. The rock elastic wave dispersion and attenuation characteristics measurement system according to claim 1, characterized in that: The bore pressure loader (13) comprises a cylinder body, a piston is installed in the cylinder body, the piston is connected to a stepper motor via a coupling, the stepper motor is also connected to a speed controller, the stepper motor and the speed controller are connected to the computer, and the pressurized medium in the bore pressure pipeline is silicone oil; the confining pressure loader (15) and the axial pressure sensor (20) have the same structure as the bore pressure loader (13).

4. The rock elastic wave dispersion and attenuation characteristics measurement system according to claim 1 is characterized by: The data acquisition box (16) has a central controller, the central controller is connected to a memory and an A / D converter, the A / D converter is connected to the strain gauge, and the central controller is connected to the computer.

5. The rock elastic wave dispersion and attenuation characteristics measurement system according to claim 1, characterized in that: The core sample (5) is wrapped with potting glue.

6. The rock elastic wave dispersion and attenuation characteristics measurement system according to claim 1, characterized in that: The ultrasonic signal generating device is made of piezoelectric ceramics.

7. A method for measuring the dispersion and attenuation characteristics of rock elastic waves, characterized in that The method uses the measurement system according to any one of claims 1 to 6, comprising the following steps: Placing the elastic wave dispersion and attenuation core sample (5) in a positioning sealing device (7); Then, the confining pressure chamber (3) is installed, and the pore pressure loader (13), the confining pressure loader (15), and the axial pressure loader (14) are started to apply pore pressure, confining pressure, and axial pressure to the core sample (5) in the positioning and sealing device (7) respectively; Starting the ultrasonic signal generating device and the exciter (12) in the probe body (6), thereby exciting the high-frequency signal and the medium- and low-frequency signals to be applied to the core sample (5); The computer collects data of the core sample (5) through a force sensor (11), a pressure relief sensor (17), a pore pressure sensor (21), a confining pressure sensor (19), and an axial pressure sensor (20); The data acquisition box (16) acquires real-time stress signals of a plurality of strain gauges and transmits them to a computer, and the computer obtains an energy spectrum of the earthquake source by performing a cross-correlation interference algorithm on two signals in the frequency domain; The attenuation characteristic curve is calculated by data acquisition and the phase difference between the continuous signals of the same frequency at any two positions in the acquired core sample (5).

8. The method for measuring rock elastic wave dispersion and attenuation characteristics according to claim 7, characterized in that: The core sample (5) is in the shape of a rectangle or a cylinder, and the strain gauges are adhered on its surface at the same distance.

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