KR100767176B1 - Method for measuring shear-wave resonance frequency using stress-wave resonance method based on flexural-wave nodal points - Google Patents

Abstract

A method for measuring a shear-wave resonance frequency in an elastic medium is provided to increase the reliability of a measured resonance frequency by measuring the resonance frequency for a shear-wave in a state of minimizing flexural-wave resonance. A method for measuring a shear-wave resonance frequency in an elastic medium includes the steps of: determining a distance d of a minimum resonance point of a flexural-wave from an end of a hollow body(1), which is composed of the elastic medium to be measured, by a formula 1 in case that the Poisson ratio of the hollow body(1) is 0.3333, by a formula 2 in case that the Poisson ratio of the hollow body(1) is 0.2, and by a formula 3 in case that the Poisson ratio of the hollow body(1) is a value except 0.2 or 0.3333; installing an accelerometer(3) which measures an acceleration signal at a minimum resonance point of one side, and generating a shear-wave to the hollow body(1) by having an impact on the minimum resonance point of the flexural-wave which exists on an opposite side to the accelerometer(3); converting the signal measured by the accelerometer(3) into a frequency domain by Fourier-transforming the measured signal, and calculating a displacement transfer function; and measuring a frequency having a maximum function value at the displacement transfer function and determining the measured frequency as the resonance frequency of the shear-wave. The formula 1 is d=0.2362xL-0.09xD, the formula 2 is d=0.2302xL-0.05xD, and the formula 3 is d=7.5(d0.333-d0.2L)(v-0.2)+d0.2.

Description

Method for Measuring Shear-Wave Resonance Frequency Using Stress-Wave Resonance Method based on Flexural-Wave Nodal Points}

1 is a schematic diagram showing a test specimen configuration used in a conventional resonant technique.

Figure 2 is a schematic diagram showing the test specimen test configuration required to perform the measuring method according to the present invention.

Figure 3a is a graph of the measurement results of the displacement transfer function measured by hitting the maximum resonant point of the bending wave to the concrete specimen in accordance with the present invention.

Figure 3b is a graph of the measurement results of the displacement transfer function measured by hitting the minimum resonant point of the bending wave in accordance with the present invention for the same specimen.

<Description of the symbols for the main parts of the drawings>

1 cylindrical specimen

2 damping plate

3 accelerometer

The present invention relates to a method for measuring the shear wave resonant frequency in a viscoelastic medium using a flexural wave node-based elastic wave resonance technique. More specifically, the present invention relates to a shear wave resonant frequency in a cylindrical specimen made of a viscoelastic medium such as concrete. The present invention relates to a method for reliably measuring the resonance frequency of a shear wave by minimizing the resonance of the flexural wave by using the fundamental mode nodal points of the flexural wave.

It is very important to accurately measure the dynamic characteristics of viscoelastic media such as rock or concrete, that is, the material decay ratio and the Young's modulus. This is because these dynamic properties of the viscoelastic medium are very useful for seismic analysis of soils, maintenance of concrete structures, and soundness evaluation.

In general, the dynamic properties of viscoelastic media such as concrete are measured using a cylindrical specimen. In other words, a test specimen of a viscoelastic medium made in a cylindrical shape is tested to measure the dynamic characteristics of the viscoelastic medium. A conventional method of measuring the dynamic characteristics of a viscoelastic medium using such a cylindrical specimen is a resonance method. In the above resonant technique, the resonant frequency of the compression wave multi-reflected in the specimen is measured to measure the dynamic characteristics (elastic modulus of elasticity, material damping ratio for the compression wave, etc.) of the specimen. Figure 1 is a schematic diagram showing the test specimen used in the conventional resonant technique, the accelerometer 11 is attached to the side of one end of the specimen 10 of the viscoelastic medium produced in a cylindrical shape so that both ends are free surfaces, A physical impact is applied by hitting one side of the specimen 10 to which the accelerometer 11 is attached with a hammer or the like. Due to such an impact, an elastic wave (compression wave) is generated in the viscoelastic medium of the specimen 10, and the compressed wave resonating between the free surfaces of both ends of the specimen 10 is measured by the accelerometer 11. After recording the compressed wave measured in this manner with a data recording device such as an oscilloscope, the resonance frequency of the specimen 10, that is, the compressed wave of the corresponding viscoelastic medium, is measured through a signal analysis process using a computer. The characteristic is measured.

However, by the above-described resonant technique, only the resonant frequency of the uncompressed compression wave, that is, the resonant frequency of the viscoelastic medium appearing when the compressed wave is applied, can not be measured, but the resonant frequency of the shear wave cannot be measured. Firstly, the resonant frequency of shear wave is very important from the ground engineering point of view. The resonant frequency of viscoelastic medium is used as the essential property for the seismic analysis of the ground. Secondly, the resonant frequency of shear wave is used for strength evaluation, quality control and soundness evaluation of concrete structures such as concrete pavement, concrete lining of tunnel, concrete deck of bridge, etc. As described above, in the viscoelastic medium, it is very important to reliably measure the resonant frequency with respect to the shear wave. However, in the conventional resonant technique, there is a problem that the resonant frequency with respect to the shear wave cannot be measured.

On the other hand, conventionally as a method for measuring the dynamic characteristics of the shear wave, that is, the resonant frequency for the shear wave, by modifying the method of measuring the resonant frequency for the compressed wave as described above, by generating a non-shear shear wave instead of the compressed wave, the resonance frequency accordingly A method of measuring the has been proposed. In this method, an auxiliary device such as a hose clamp or an ultra-small aluminum square bar is attached to one end of the cylindrical specimen to apply instantaneous force, and then the same measurement and signal processing as the method of measuring the resonance frequency of the compressed wave is performed. Through the process, the resonance frequency is measured.

However, in the measurement method using the non-frequency shear wave, various auxiliary devices are used when applying the instantaneous non-stress force, and thus the measured signal is affected by these auxiliary devices, and as a result, the result measured by this method is There is a problem that the reliability is low because a significant error is included.

The present invention has been developed to solve the problems of the conventional method as described above, in measuring the resonant frequency of the shear wave of the viscoelastic medium, caused by the auxiliary device used to apply the instantaneous torsional force on the cylindrical specimen It is an object of the present invention to provide a resonant frequency measurement method using a shear wave of a new method that can eliminate measurement errors and obtain a reliable measurement result by a simple method.

In order to achieve the above object, in the present invention, the calculation formula is selected according to the Poisson's ratio of the cylindrical specimen consisting of a viscoelastic medium to be measured and both ends are free ends to the minimum resonance point of the bending wave from the one end of the specimen. Determining a distance; Installing an accelerometer for measuring an acceleration signal at the minimum resonant point on one side, and generating a shear wave to the specimen by applying an impact to a minimum resonant point of a bending wave existing on the opposite side where the accelerometer is not installed; Calculating a displacement transfer function by Fourier transforming the signal measured by the accelerometer to a frequency domain; A method for measuring shear wave resonant frequency in a viscoelastic medium is provided, comprising measuring the frequency at which the function value becomes the maximum in the displacement transfer function and determining it as the resonant frequency of the shear wave.

In the measuring method of the present invention as described above, the center of the center between the minimum resonant point of the bending wave in the cylindrical specimen as the maximum resonant point of the bending wave, giving a shock to the maximum resonance point of the bending wave to generate a shear wave in the specimen, at this time Measuring the resonant frequency of the bending wave by Fourier transforming the measured signal into a frequency domain to obtain a displacement signal, calculating a displacement transfer function, and measuring a frequency at a point where the amplitude of the displacement transfer function is obtained; And comparing the measured resonant frequency of the bending wave with the measured resonant frequency of the shear wave and determining whether the same is the same.

Hereinafter, a method for measuring resonance frequency by shear wave according to an embodiment of the present invention will be described with reference to the accompanying drawings.

Figure 2 is a schematic diagram showing the test specimen test configuration required to perform the measuring method according to the present invention.

In the present invention, after the cylindrical specimen (1) consisting of the viscoelastic medium to be measured, the position where the accelerometer (3) is mounted and the position at which the specimen (1) is to be impacted to generate a shear wave is determined by a special calculation, By measuring the specific impact position of the specimen 1 with the accelerometer 3 attached to the determined mounting position, a shear wave is applied to the specimen 1, and measuring and processing the data according to the accelerometer 3 so that the measurement target The resonance frequency caused by the shear wave of the viscoelastic medium is measured.

  Specifically, as shown in Figure 2, first prepare a cylindrical specimen 1 made of a viscoelastic medium to be measured. At the time of measurement, the cylindrical specimen 1 is preferably placed on the damping plate 2 made of a material that damps the bending wave, such as urethane.

In the present invention, in order to measure the resonance frequency due to the shear wave with high reliability, the operation to minimize the bending wave resonance is performed. To this end, in the present invention, the position at which the resonance of the bending wave is minimized and the position at the maximum in the specimen 1 is determined. That is, the positions of the minimum resonance points N1 and N3 and the maximum resonance point N2 of the bending wave are determined.

When the bending wave propagates or reflects in the specimen 1, resonance waves occur in the case of the bending wave having a specific frequency. The resonance phenomenon of a bending wave having the smallest frequency among the various frequencies in which such a resonance occurs is called a "fundamental mode". In the fundamental mode of the bending wave, a bending displacement is caused by the bending mode. There is a point that becomes zero, that is, a nodal point. The fracture point in the basic mode of the bending wave becomes the minimum resonance point of the bending wave when the bending wave is applied to the specimen 1. In the cylindrical specimen 1, there are two such fracture points, that is, the minimum resonant points of the bending wave.

 The inventor of the present invention has derived a formula for determining the position of the minimum resonant point of the bending wave through the finite element analysis, the position of the minimum resonant point of the bending wave, that is, the minimum resonance point of the bending wave (N1, from one end of the cylindrical specimen 1) The distance d to N3) is determined by Equation 1 or 2 below. Here, whether to use Equation 1 or Equation 2 is determined according to the Poisson's ratio of the cylindrical specimen. When the Poisson's ratio is 0.3333, d is obtained using Equation 1, and when the Poisson's ratio is 0.2, The d is obtained by using Equation 2, and when the Poisson's ratio is not the above two values, the d is obtained by using Equation 3. As described above, in the present invention, in the cylindrical specimen 3, the positions spaced apart from the both ends of the specimen 3 by a distance d, respectively, are taken as the minimum resonance points N1 and N3 of the bending wave.

On the other hand, the point where the maximum displacement occurs in the fundamental mode of the bending wave is the maximum resonance point, in the present invention, in the cylindrical specimen 1, the center of the minimum resonance point (N1, N3) of the bending wave is the maximum resonance point of the bending wave ( N2).

In Equations 1 and 2, L is the total length of the cylindrical specimen, D is the diameter of the cylindrical specimen. In Equation 3, d _0.3333 is a distance d from one end of the cylindrical specimen 1 when the Poisson's ratio is 0.3333 to the minimum resonance points N1 and N3 of the bending wave, and d _0.2 is a cylindrical shape when the Poisson's ratio is 0.2. The distance d from one side end of the specimen 1 to the minimum resonance points N1 and N3 of the bending wave, and υ is the Poisson's ratio.

In FIG. 2, the minimum resonance point of the bending wave is indicated by N1, the maximum resonance point of the bending wave is indicated by N2, and the bending wave from one end of the specimen 1 obtained by Equation 1, Equation 2 or Equation 3 above. The distances d to the minimum resonance points N1 and N3 are indicated respectively. In FIG. 2, reference numeral L denotes the total length of the specimen 1, and the arrows on N2 and N3 denote the strike direction of the measurement hammer.

In the present invention, one of the minimum resonance points N1 and N3 of the bending wave in the cylindrical specimen 1 determined as described above becomes the acceleration signal measurement position, and the other becomes the shear wave generation position. That is, after determining the positions of the minimum resonance points N1 and N3 and the maximum resonance point N2 of the bending wave in the cylindrical specimen 1 as described above, the accelerometer 3 is installed at the minimum resonance point N1 on one side, and A shear wave is generated in the specimen 1 by impacting the minimum resonance point N3 of the bending wave existing on the opposite side where the accelerometer 3 is not provided with a measuring hammer or the like. The accelerometer 3 measures the acceleration signal generated in the specimen 1 by such an impact, and the measurement signal is recorded using a known signal recording device such as an oscilloscope.

In the present invention, the resonance acceleration due to the shear wave is determined by obtaining the displacement transfer function from the signal measured by the accelerometer 3 as described above. In short, the displacement transfer function is calculated by Fourier transforming the signal measured by the accelerometer 3 into the frequency domain. Specifically, since the signal measured by the accelerometer 3 is an acceleration signal in the time domain, it is Fourier transformed into the frequency domain. Subsequently, the Fourier transformed signal is integrated twice in the frequency domain to obtain a displacement signal, and the displacement transfer function is obtained by dividing the Fourier transformed signal by the impact acceleration signal applied to the specimen 1 to generate the impact acceleration signal. . The acceleration signal of the impact applied to the specimen 1 is measured through an accelerometer provided in the measuring hammer.

Subsequently, the resonance frequency is determined using the maximum amplitude of the displacement transfer function. The frequency at which the amplitude of the displacement transfer function becomes maximum becomes the resonance frequency of the shear wave.

As described above, in obtaining the resonance frequency of the shear wave, in the present invention, unlike the conventional technique of applying the torsional shear wave to the specimen by using an auxiliary device and measuring the resonance frequency accordingly, the flexural wave in the specimen is based on the fundamental mode of the bending wave. The resonance frequency of the specimen with respect to the shear wave is measured by using the minimum resonant point of the bending wave, which minimizes the resonance, as the measurement position of the acceleration and the generation position of the shear wave. Therefore, in the present invention, the resonance frequency of the shear wave can be measured in a state in which the bending wave resonance is minimized, and thus the reliability of the measured resonance frequency is very high.

On the other hand, in some cases, it may be unclear whether the point where the amplitude of the displacement transfer function due to the bending wave minimum resonant point strike obtained through the above method is maximized is the resonance frequency for the shear wave. This is the case, for example, when the amplitude of the displacement transfer function peaks at multiple points. In this situation, to make it easier for the measurer to determine the resonant frequency of the shear wave, the following steps are taken to measure the resonant frequency of the flexural wave and compare it with the amplitude measurement of the displacement transfer function obtained earlier. You can also proceed.

Specifically, the cylindrical specimen 3 impacts the maximum resonance point N2 of the bending wave to generate a shear wave in the specimen 3, and then obtains the resonance frequency of the bending wave from the measured signal. That is, in the same manner as in the process of measuring the resonance frequency of the shear wave by impacting the minimum resonance point N3 of the bending wave, the bending wave using the measuring hammer or the like while the accelerometer 3 is installed at the minimum resonance point N3 of the bending wave. The shear wave is generated by hitting the maximum resonance point (N2) of and the signal is measured by the accelerometer (3). Fourier transform the acceleration signal in the time domain measured by the accelerometer (3) to convert it into the frequency domain.Integrate it twice in the frequency domain to obtain the displacement signal, then divide it by the acceleration signal to find the displacement transfer function. The resonance frequency of the bending wave is measured by measuring the frequency at the point where the amplitude of the displacement transfer function is obtained.

When the resonance frequency of the bending wave measured in this way is compared with the frequency at which the amplitude of the displacement transfer function due to the strike of the bending wave minimum resonance point is measured, the amplitude of the displacement transfer function becomes a peak, not the resonance frequency of the bending wave. It is easy to confirm that the frequency is a resonant frequency caused by the shear wave.

Figure 3a, b is a graph showing the measurement results of the displacement transfer function measured by the test according to the present invention for the cylindrical specimen made of concrete, Figure 3a is measured by hitting the maximum resonance point (N2) of the bending wave Fig. 3b is a graph showing the measurement result of the displacement transfer function measured by hitting the minimum resonance point N2 of the bending wave against the same specimen. In FIG. 3A, the frequency at which the displacement transfer function peaks is 3544.9 Hz. This value corresponds to the resonance frequency of the flexural wave of the test specimen, that is, the concrete. On the other hand, in Figure 3b, there are two points where the value of the displacement transfer function peaks, one of which is not so high, and the frequency at this time is 3544.9 Hz, and the frequency at the point where the relatively high peak is 3773.4 Hz. . Of these, 3544.9 Hz is the same as the resonant frequency of the flexural wave, and 3773.4 Hz, which is not this value, is the resonant frequency of the shear wave.

As described above, the cylindrical specimen 3 impacts the maximum resonance point N2 of the bending wave to generate a shear wave in the specimen 3, and then obtains the resonance frequency of the bending wave from the measured signal. When compared with the peak values of the displacement transfer function obtained from the signal measured by shocking (N3), which of the peak values of the displacement transfer function obtained from the signal measured by impacting the minimum resonance point (N3) of the bending wave is determined. The resonance frequency can be easily identified.

The resonance frequency of the shear wave measured according to the method of the present invention can be used to measure the dynamic properties of the viscoelastic medium to be measured.

As described above, in obtaining the resonant frequency of the shear wave, in the present invention, unlike the conventional technique of applying the torsional shear wave to the specimen using an auxiliary device and measuring the resonance frequency accordingly, the specimen is based on the fundamental mode of the bending wave. The resonance frequency of the specimen with respect to the shear wave is measured by using the minimum resonance point of the bending wave in which the resonance of the bending wave is minimized as the measurement position of the acceleration and the generation position of the shear wave, respectively. Therefore, in the present invention, the resonance frequency of the shear wave can be measured in a state in which the bending wave resonance is minimized, and thus the reliability of the measured resonance frequency is very high.

In the above described the configuration and features of the present invention based on the embodiment according to the present invention, the present invention is not limited to this, it is possible to be freely modified according to the technical idea of the present invention.

Claims (2)

When the Poisson's ratio of the cylindrical specimen 1 consisting of a viscoelastic medium to be measured and having free ends is 0.3333, by Equation 1, when Poisson's ratio is 0.2, and by Poisson's ratio 0.2 Or b if the value is anything other than 0.3333, determining the distance d from one end of the specimen (1) to the minimum resonance points (N1, N3) of the bending wave by Equation (3); An accelerometer (3) for measuring an acceleration signal is installed at the minimum resonant point (N1) on one side, and the shear wave is applied by applying an impact to the minimum resonant point (N3) of the bending wave existing on the opposite side where the accelerometer (3) is not provided. Generating on the specimen 1; Calculating a displacement transfer function by Fourier transforming the signal measured by the accelerometer (3) to a frequency domain; And measuring the frequency at which the function value becomes the maximum in the displacement transfer function and determining the frequency as the resonance frequency of the shear wave. (Equation 1)

(Equation 2)

(Equation 3)

(Where L is the total length of the cylindrical specimen 1, D is the diameter of the cylindrical specimen 1, and d _0.3333 is the minimum resonant point of the bending wave from one end of the cylindrical specimen 1 when the Poisson's ratio is 0.3333). The distance d to (N1, N3), d _0.2 is the distance d from one end of the cylindrical specimen 1 to the minimum resonance point (N1, N3) of the bending wave when the Poisson's ratio is 0.2, υ is the Poisson's ratio ) The method of claim 1,  In the cylindrical specimen 1, the center between the minimum resonance points N1 and N3 of the bending wave is taken as the maximum resonance point N2 of the bending wave, and the impact is given to the maximum resonance point N2 of the bending wave, thereby shearing the specimen 1 with the shear wave. After generating the signal, Fourier transform the measured signal into the frequency domain to obtain the displacement signal, calculate the displacement transfer function, and measure the frequency of the point that becomes the amplitude of the displacement transfer function to measure the resonant frequency of the bending wave. step; And And comparing the measured resonant frequency of the flexural wave with the measured resonant frequency of the shear wave and determining whether the same is the same.

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