JP2017166922A - Natural frequency detection method of structure and natural frequency detection method of structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a natural frequency detection method of a structure for more reliably detecting a change with time of the natural frequency of the structure.SOLUTION: A natural frequency detection method S1 for detecting a natural frequency of a structure arranged on a support obtains an initial natural frequency which is the initial natural frequency of the structure, and includes a frequency detection step S8 for detecting the frequency in the direction orthogonal to the frequency in a horizontal direction along a horizontal surface by a frequency sensor located above the support in the structure at a first time; a coherence calculation step S10 for obtaining a change in coherence function by the frequency with the frequency in the horizontal direction and the frequency in the vertical direction as an input; and a natural frequency specifying step S12 for defining the frequency corresponding to a peak value of the coherence function most close to the initial natural frequency in value as the natural frequency of the structure at the first time.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a natural frequency detection method for a structure and a natural frequency detection device for a structure.

Conventionally, in order to specify the natural frequency of a structure such as a pier, an impact vibration test is generally performed. In the impact vibration test, the accuracy of the specified natural frequency is high. However, the impact vibration test is dangerous and the impact vibration test is not suitable for constantly monitoring the natural frequency.
On the other hand, for example, a pier soundness evaluation system described in Patent Document 1 is known as a method aiming to constantly monitor the natural frequency.

  In this pier soundness evaluation system, paying attention only to the peak of the Fourier spectrum obtained from the vibration measured by the vibration detector (vibration sensor) provided at the top (top) of the pier, the frequency at which the peak is shown Is regarded as the natural frequency. When the natural frequency exceeds the threshold value, it is evaluated that the pier is stable, and when the natural frequency is below the threshold value, it is evaluated that the pier is unstable.

Japanese Patent No. 4698466

  However, in cases such as cases that are strongly affected by the vibration of the incidental structure or the ground, there are cases where many peaks other than the natural frequency are dominant and the natural frequency cannot be specified correctly.

  The present invention has been made in view of such problems, and is a method for detecting a natural frequency of a structure and a natural frequency of the structure that can more reliably detect changes in the natural frequency of the structure over time. An object is to provide a detection device.

In order to solve the above problems, the present invention proposes the following means.
The natural frequency detection method for a structure according to the present invention is a method for detecting the natural frequency of a structure for detecting the natural frequency of a structure arranged on a support, and the initial natural frequency of the structure is as follows. A vibration detection step of obtaining an initial natural frequency and detecting a horizontal vibration and a vertical vibration along a horizontal plane at a first time by a vibration sensor mounted above the support in the structure. And a coherence calculation step for obtaining a change in coherence function depending on the frequency by using the horizontal vibration and the vertical vibration as inputs, and a peak value of the coherence function closest to the initial natural frequency. And a natural frequency specifying step of setting the frequency as the natural frequency of the structure at the first time.

  Further, the natural frequency detection device for a structure according to the present invention is a natural frequency detection device for a structure for detecting a natural frequency of a structure disposed on a support, and the support in the structure And a control unit that calculates a natural frequency of the structure based on a detection result of the vibration sensor, and the control unit uses the vibration sensor to detect a first time. The horizontal vibration along the horizontal plane detected in the horizontal plane and the vertical vibration are input, and the change of the coherence function according to the frequency is obtained, and the coherence closest to the initial natural frequency of the structure obtained in advance is obtained. The frequency corresponding to the peak value of the function is the natural frequency of the structure at the first time.

  According to these inventions, the change of the coherence function by the frequency with the vibration in the horizontal direction and the vibration in the vertical direction detected by the vibration sensor at the first time as input is obtained. Then, the frequency corresponding to the peak value of the coherence function closest to the initial natural frequency is set as the natural frequency of the structure at the first time. Even when trying to identify the natural frequency of the structure from the Fourier spectrum of the vibration, there are cases where many peaks other than the natural frequency are prominent and the natural frequency of the structure cannot be correctly identified. By obtaining the natural frequency of the structure from the coherence function, it is possible to reliably identify the natural frequency of the structure at the first time and more reliably detect changes in the natural frequency of the structure over time. .

In the above-described method for detecting the natural frequency of a structure, the vibration sensor may be attached to an end of the upper surface of the structure.
According to the present invention, since the structure vibrates around the lower part of the structure, the amplitude of the vibration of the structure is the largest on the upper surface. For this reason, vibration can be detected more reliably by the vibration sensor.

In the method for detecting the natural frequency of the structure, the vibration detection step, the coherence calculation step, and the natural frequency identification step may be performed a plurality of times.
According to this invention, the natural frequency of the structure can be continuously detected a plurality of times.

Further, the natural frequency detection method for a structure according to the present invention is a natural frequency detection method for a structure for detecting a natural frequency of a structure disposed on a support, wherein the initial natural frequency of the structure is detected. The initial natural frequency, which is the frequency, is obtained, the first vibration sensor and the second vibration sensor are mounted above the support in the structure, and the first vibration sensor is mounted on the structure. The angle between the line connecting the rotation center of the structure and the vertical direction is α, and the line connecting the position where the second vibration sensor is attached to the structure and the rotation center is the vertical direction. The angle is β, the vibration at the first time in the horizontal direction along the horizontal plane detected by the first vibration sensor is Ax, and the vibration at the first time in the vertical direction detected by the first vibration sensor is Az. Detected by the second vibration sensor A support body vibration calculation step for obtaining the horizontal vibration Gx of the support body at the first time by the equation (1), where Bz is the vibration at the first time in the vertical direction; In the relationship of the phase difference between the vibration Ax and the vibration Gx with respect to the frequency, the frequency when the phase difference is π / 2 radians in the range where the phase difference changes from 0 radians to π radians, and the phase difference is The frequency closest in value to the initial natural frequency among the frequencies when the phase difference is −π / 2 radians in a range that changes from 0 radians to −π radians is determined at the first time. And a natural frequency specifying step for setting the natural frequency of the structure.
Gx = Ax− (Az−Bz) / (tan α + tan β) (1)

Further, the natural frequency detection device for a structure according to the present invention is a natural frequency detection device for a structure for detecting a natural frequency of a structure disposed on a support, and the support in the structure A first vibration sensor and a second vibration sensor mounted above the control, and a control for calculating a natural frequency of the structure based on detection results of the first vibration sensor and the second vibration sensor An angle formed by a line connecting a position where the first vibration sensor is attached to the structure and the rotation center of the structure and a vertical direction is α, and the second vibration sensor is the structure. The horizontal plane detected by the first vibration sensor at a first time when the angle formed by the line connecting the position attached to the object and the rotation center and the vertical direction is β. Horizontal vibration Ax along the vertical direction From the Az and the vertical vibration Bz detected at the first time by the second vibration sensor, the horizontal vibration Gx of the support at the first time is obtained by the equation (2). In the relationship of the phase difference between the vibration Ax and the vibration Gx with respect to the frequency, the frequency when the phase difference is π / 2 radians in a range where the phase difference changes from 0 radians to π radians, and Among the frequencies when the phase difference is -π / 2 radians in a range where the phase difference changes from 0 radians to -π radians, the value of the initial natural frequency of the structure obtained in advance is the largest. The close frequency is the natural frequency of the structure at the first time.
Gx = Ax− (Az−Bz) / (tan α + tan β) (2)

According to these inventions, the vibrations detected by the two vibration sensors are each affected by the vibration of the ground. For this reason, by calculating the difference between the vibrations of the two vibration sensors, the vibration of the structure itself that suppresses the influence of the vibration of the ground can be obtained. Generally, the phase difference between the horizontal vibration of the structure and the horizontal vibration of the support is inverted at a frequency near the natural frequency of the structure.
The phase difference at the first time is obtained, and the frequency at which this phase difference is ± π / 2 radians is defined as the natural frequency of the structure. Thereby, it is possible to reliably specify the natural frequency of the structure at the first time and more reliably detect a change in the natural frequency of the structure with time.

In the method for detecting the natural frequency of the structure, the first vibration sensor and the second vibration sensor may be attached to an upper surface of the structure.
According to the present invention, since the structure vibrates around the lower part of the structure, the amplitude of the vibration of the structure is the largest on the upper surface. For this reason, vibration can be detected more reliably by the first vibration sensor and the second vibration sensor.

In the method for detecting the natural frequency of the structure, the support vibration calculation step and the natural frequency specifying step may be performed a plurality of times.
According to this invention, the natural frequency of the structure can be continuously detected a plurality of times.

  According to the natural frequency detection method of a structure and the natural frequency detection device of a structure of the present invention, it is possible to more reliably detect a change with time of the natural frequency of the structure.

It is a perspective view which shows the outline | summary of the bridge used as the object which detects the natural frequency with the natural frequency detection apparatus of the structure of 1st Embodiment of this invention. It is a block diagram of the natural frequency detection apparatus of the structure. It is a flowchart which shows the natural frequency detection method of the structure of 1st Embodiment of this invention. It is a figure which shows an example of the Fourier spectrum of the vibration of the bridge axis orthogonal direction detected with the natural frequency detection method of the structure. It is a figure which shows an example of the change of the coherence function by the frequency calculated | required with the natural frequency detection method of the structure. It is a block diagram of the natural frequency detection apparatus of the structure of 2nd Embodiment of this invention. It is a figure for demonstrating prescription | regulations, such as the length and angle of a bridge pier and a vibration sensor. It is a flowchart which shows the natural frequency detection method of the structure of 2nd Embodiment of this invention. It is a figure which shows an example of the Fourier spectrum of the vibration of the bridge axis orthogonal direction detected with the natural frequency detection method of the structure. It is a figure which shows an example of the phase difference of the vibration Ax with respect to the frequency calculated | required with the natural frequency detection method of the structure, and the vibration Gx. It is a figure which shows an example of the phase difference with respect to the frequency obtained by the experiment for confirming the natural frequency detection method of the structure. The acceleration between the direction perpendicular to the bridge axis and the acceleration in the vertical direction detected by the first vibration sensor upstream of the river flow obtained in an experiment to confirm the natural frequency detection method of the structure. It is a figure which shows a relationship. The acceleration between the direction perpendicular to the bridge axis and the acceleration in the vertical direction detected by the second vibration sensor downstream of the river flow obtained in an experiment to confirm the natural frequency detection method of the structure. It is a figure which shows a relationship. It is a figure which shows the difference between the vibration of the estimated ground obtained by the experiment for confirming the natural frequency detection method of the structure, and the vibration of the actually measured ground in relation to the vibration frequency and the acceleration spectrum. . It is a figure which shows the difference of the vibration of the estimated ground obtained by the experiment for confirming the natural frequency detection method of the structure, and the vibration of the ground actually measured by the relationship between a frequency and a phase difference. . The vibration measured in the experiment to confirm the natural frequency detection method of the same structure, the vibration in the direction perpendicular to the bridge axis at the end of the upper surface of the bridge pier and the vibration in the direction perpendicular to the bridge axis measured in the ground It is a figure which shows the relationship between the Fourier spectrum ratio by and frequency. Based on the vibration measured in the experiment at the end of the top of the bridge pier in the direction perpendicular to the bridge axis and the estimated vibration in the direction perpendicular to the bridge axis of the ground obtained in an experiment to confirm the natural frequency detection method of the structure. It is a figure which shows the relationship between a Fourier spectrum ratio and a frequency.

(First embodiment)
Hereinafter, a first embodiment of a natural frequency detection device (hereinafter also simply referred to as a detection device) of a bridge pier (structure) according to the present invention will be described with reference to FIGS. 1 to 5.
As shown in FIGS. 1 and 2, the present detection device 1 is for detecting the natural frequency of a pier B1 of a bridge B disposed on a riverbed (support) R2a that is the ground. Hereinafter, a case where the bridge B is a railway bridge will be described as an example. In FIG. 2, only the pier B1 of the bridge B is shown.
The bridge B is configured such that a bridge girder B2 is supported on bridge piers B1 arranged at intervals in the bridge axis direction Y. A track B3 is fixed on the bridge beam B2. The bridge beam B2 and the track B3 extend in the bridge axis direction Y, and the width direction of the track B3 becomes the bridge axis perpendicular direction (horizontal direction) X. The bridge axis direction Y and the bridge axis perpendicular direction X are, for example, directions along a horizontal plane.
The pier B1 is made of a rigid body such as stone, brick, or concrete. The bridge beam B2 and the track B3 are mainly formed of steel.

  As shown in FIG. 2, the foundation B5 provided at the lower part of the pier B1 is fixed to the riverbed R2 indicated by a two-dot chain line of the river R1 in the initial stage. When the scouring S in which the river bottom R2 around the foundation B5 is scooped out by the water flowing through the river R1, the shape of the river bottom R2 becomes the river bottom R2a. The pier B1 where the scouring S has occurred becomes unstable with respect to the riverbed R2a.

The detection apparatus 1 includes a vibration sensor 11 attached to the upper surface B1a of the pier B1, and a control unit 16 that calculates the natural frequency of the pier B1 based on the detection result of the vibration sensor 11.
As the vibration sensor 11, for example, a known speed sensor or acceleration sensor that can detect vibration (speed or acceleration) in two directions orthogonal to each other can be used. The vibration sensor 11 is attached to the end of the upper surface B1a of the pier B1 above the riverbed R2a in the pier B1. The vibration sensor 11 outputs the detected vibration as, for example, a potential difference.
The control unit 16 includes an arithmetic circuit 18, a memory 19, an input unit 20, a display unit 21, and an input / output I / F (interface) 22 connected to the bus 17.
The arithmetic circuit 18 has a central processing unit (CPU) and the like.
As the memory 19, a ROM (Read Only Memory) or a RAM (Random Access Memory) is used. The memory 19 stores a program for controlling the arithmetic circuit 18 and the like. The program includes a program for performing fast Fourier transform, which will be described later, and calculating a coherence function.

The input unit 20 includes a keyboard (not shown) and a pointing device such as a mouse. An instruction input from the keyboard or the like by the user is transmitted from the input unit 20 to the arithmetic circuit 18.
The display unit 21 includes a liquid crystal panel (not shown). The display unit 21 displays the signal transmitted from the arithmetic circuit 18 on the liquid crystal panel.
The input / output I / F 22 corresponds to a standard such as USB (Universal Serial Bus). The vibration sensor 11 can be connected to the input / output I / F 22.
As the control unit 16 having the bus 17, the arithmetic circuit 18, the memory 19, the input unit 20, the display unit 21, and the input / output I / F (interface) 22, a known personal computer can be used.

Next, the operation of the present detection apparatus 1 configured as described above will be described. FIG. 3 is a flowchart showing a natural frequency detection method (hereinafter also simply referred to as a detection method) S1 of the pier in the first embodiment of the present invention. When the detection apparatus 1 is activated, the arithmetic circuit 18 of the control unit 16 reads a program stored in the memory 19.
First, in the initial natural frequency specifying step (step S6, see FIG. 3), the user performs a known impact load test or the like to obtain in advance an initial natural frequency that is an initial natural frequency of the pier B1. For example, assume that the initial natural frequency is determined to be 18 Hz (Hertz). The user inputs this initial natural frequency from the input unit 20 while confirming the display on the display unit 21 and stores it in the memory 19 of the control unit 16.
Next, in the vibration detection step (step S8), the vibration sensor 11 detects the vibration in the direction X perpendicular to the bridge axis and the vibration in the vertical direction Z at the first time. The horizontal direction may be the bridge axis direction Y, or the direction between the bridge axis perpendicular direction X and the bridge axis direction Y. The vibration sensor 11 converts each detected vibration into a signal and transmits the signal to the control unit 16.

Next, in the coherence calculation step (step S10), the calculation circuit 18 of the control unit 16 uses the vibration in the direction perpendicular to the bridge axis X and the vibration in the vertical direction Z as inputs, and obtains a change in the coherence function depending on the frequency.
Specifically, the user attaches the vibration sensor 11 to the upper surface B1a of the pier B1. To attach the vibration sensor 11 to the pier B1, a known adhesive or the like can be used. Since the pier B1 vibrates around the lower part of the pier B1, the vibration amplitude of the pier B1 is the largest on the upper surface B1a. For this reason, the vibration sensor 11 detects the vibration of the pier B1 more reliably.
The vibration in the direction perpendicular to the bridge axis X detected by the vibration sensor 11 and the vibration in the vertical direction Z are fast Fourier transformed to calculate the Fourier spectrum of each vibration. FIG. 4 shows an example of the Fourier spectrum of the vibration in the direction X perpendicular to the bridge axis. The horizontal axis in FIG. 4 represents the frequency (Hz), and the vertical axis represents the acceleration spectrum (μm / s · s).
In the Fourier spectrum of the vibration in FIG. 4, many peaks other than the natural frequency are dominant, and it is difficult to specify the peak value of the acceleration spectrum whose value is close to the initial natural frequency ω ₀ of 18 Hz. Generally, when scouring S occurs on the pier B1, the natural frequency becomes smaller than the initial natural frequency. For example, it is defined that the scouring S is considered to have occurred when the natural frequency is reduced by 20 to 30% from the initial natural frequency.

  The arithmetic circuit 18 calculates a change in the coherence function according to the frequency obtained by inputting the vibration in the direction perpendicular to the bridge axis X and the vibration in the vertical direction Z using a program for calculating the coherence function. FIG. 5 shows changes in the coherence function depending on the frequency. The horizontal axis in FIG. 5 represents the frequency (Hz), and the vertical axis represents the coherence. Coherence takes a value between 0 and 1, and the correlation between variables increases as the value approaches 1. The vibration in the direction perpendicular to the bridge axis X and the vibration in the vertical direction Z detected by the vibration sensor 11 are affected by the bridge beam B2 and the track B3, so the coherence is unlikely to be 1.

Next, in the natural frequency specifying step (step S12), the frequency corresponding to the peak value of the coherence function closest to the initial natural frequency ω ₀ is set as the natural frequency of the pier B1 at the first time. . Specifically, in the vicinity of the initial natural frequency ω _{0 of} 18 Hz in FIG. 5, the frequency ω _a of about 11.4 Hz and the frequency ω _{b of} about 17.6 Hz are the peak values of the coherence function. When | x | represents the absolute value of the variable x, | ω _a −ω ₀ | is about 6.6 Hz, and | ω _b −ω ₀ | is about _0.4 Hz. Therefore, vibration frequency omega ₁ corresponding to the peak value of the initial natural frequency omega ₀ closest coherence function value, the absolute value of the difference between the frequency and the initial natural frequency omega ₀ corresponding to the peak value is most small ones, is about 17.6Hz of vibration number ω _b. This frequency ω ₁ is the natural frequency of the pier B1 at the first time. In this case, since the reduction rate of the natural frequency is 0.02 from the equation (18-17.6) / 18, it is determined that no scouring S has occurred, for example.
Thus, the soundness of the pier B1 is evaluated.

Above, all the processes of this detection method S1 are complete | finished. Thus, the natural frequency of the pier B1 is the initial natural frequency ω ₀ , and the natural frequency ω ₁ at the _first time and the change of the natural frequency of the pier B1 with time are detected.

If necessary, after the initial natural frequency identification step S6, the vibration detection step S8, the coherence calculation step S10, and the natural frequency identification step S12 may be performed a plurality of times. That is, in the vibration detection step S8, the vibration in the direction perpendicular to the bridge axis X and the vibration in the vertical direction Z at the second time after the first time are detected, and in the coherence calculation step S10, the change in the coherence function according to the frequency is detected. Ask. In the natural frequency specifying step S12, the natural frequency of the pier B1 at the second time is calculated. By performing steps S8, S10, and S12 a plurality of times, the natural frequency of the pier B1 at the third time, the fourth time,... After the second time is calculated.
By performing this detection method S1 in this way, the natural frequency of the pier B1 is continuously detected a plurality of times.

As described above, according to the detection device 1 and the detection method S1 of the present embodiment, the vibration using the vibration in the direction perpendicular to the bridge axis X and the vibration in the vertical direction Z detected by the vibration sensor 11 at the first time is input. Find the change in coherence function by number. Then, the frequency ω ₁ corresponding to the peak value of the coherence function closest to the initial natural frequency ω ₀ is set as the natural frequency of the pier B1 at the first time. Even when trying to identify the natural frequency of the pier B1 from the Fourier spectrum of the vibration, there are cases where many peaks other than the natural frequency are prominent and the natural frequency of the pier B1 cannot be correctly identified. By obtaining the natural frequency of the pier B1 from the coherence function, it is possible to reliably identify the natural frequency of the pier B1 at the first time, and more reliably detect changes in the natural frequency of the pier B1 over time. .

Since this detection method S1 is based on the case where the vibration is very small, once the vibration sensor 11 is attached to the pier B1, the subsequent work in the vicinity of the pier B1 at the site becomes unnecessary, and the user's Safety can be ensured.
Further, since the natural frequency of the pier B1 can be estimated more accurately as compared with the detection method based on the case where the conventional vibration is very small, the soundness of the pier B1 can be accurately evaluated.

The vibration sensor 11 is attached to the upper surface B1a of the pier B1. Since the pier B1 vibrates around the lower part of the pier B1, the amplitude of the upper surface B1a is the largest among the vibration amplitudes of the pier B1. For this reason, the vibration can be detected more reliably by the vibration sensor 11.
By performing the vibration detection step S8, the coherence calculation step S10, and the natural frequency specifying step S12 a plurality of times, the natural frequency of the pier B1 can be continuously detected a plurality of times.

(Second Embodiment)
Next, a second embodiment of the present invention will be described with reference to FIGS. 6 to 17, but the same parts as those of the above-described embodiment will be denoted by the same reference numerals and the description thereof will be omitted, and only differences will be described. explain.
As shown in FIG. 6, the detection device 2 of the present embodiment replaces the vibration sensor 11 and the control unit 16 of the detection device 1 of the first embodiment with a first vibration sensor 31, a second vibration sensor 32, And a control unit 36.

The vibration sensors 31 and 32 are configured in the same manner as the vibration sensor 11. The vibration sensors 31 and 32 are attached to the end portion of the upper surface B1a of the pier B1 above the riverbed R2a in the pier B1. For example, the first vibration sensor 31 is attached to one end (upstream) of the bridge axis perpendicular direction X of the upper surface B1a, and the second vibration sensor 32 is the other (downstream) of the bridge axis perpendicular direction X of the upper surface B1a. At the end of the side. The vibration sensors 31 and 32 can be connected to the input / output I / F 22.
The control unit 36 includes a memory 37 instead of the memory 19 of the control unit 16. The program stored in the memory 37 includes a program for performing fast Fourier transform, which will be described later, and detecting inversion of a phase difference.

Here, the length and angle of the bridge pier B1 and the vibration sensors 31, 32 are defined as shown in FIG.
Let C be the center of rotation when the pier B1 vibrates. The positions where the vibration sensors 31 and 32 are attached on the upper surface B1a of the pier B1 are defined as P1 and P2. It is assumed that the vibration sensors 31 and 32 are arranged at the same height. A reference plane T passing through the center of rotation C and parallel to the horizontal plane is defined. Points where the positions P1 and P2 are projected in the vertical direction Z with respect to the reference plane T are defined as P1a and P2a. The distance in the vertical direction Z from the rotation center C to the vibration sensors 31 and 32 is defined as h (m). The angle between the line L1 connecting the position P1 and the rotation center C and the vertical direction Z is α (radian), and the angle between the line L2 connecting the position P2 and the rotation center C and the vertical direction Z is β (radian). And
When the bridge pier B1 vibrates, the inclination of the tangent at the position P1 of the locus along which the first vibration sensor 31 moves around the rotation center C is defined as a. When the bridge pier B1 vibrates, the inclination of the tangent at the position P2 of the locus along which the second vibration sensor 32 moves around the rotation center C is set to −b. However, a and b are positive numbers. The inclination a is the amount of change in the vertical direction Z when the tangent at the position P1 changes by 1 in the bridge axis perpendicular direction X. The inclination -b is the amount of change in the vertical direction Z when the tangent at the position P2 changes by 1 in the direction X perpendicular to the bridge axis.

The direction perpendicular to the bridge axis X is positive in the direction from the upstream side to the downstream side. The vertical direction Z is positive in the direction from the bottom to the top. At this time, the relationship of Formula (3) and Formula (4) is established.
tan α = a (3)
tan β = b (4)
The distance between the rotation center C and the point P1a and the distance between the rotation center C and the point P2a are obtained as in the expressions (5) and (6).
h × tan α = ah (5)
h × tan β = bh (6)
That is, the rotation center C is a point that internally divides the points P1a and P2a into a: b.

The vibration (vibration waveform) in the direction X perpendicular to the bridge axis detected by the first vibration sensor 31 is Ax. Similarly, the vibration in the vertical direction Z detected by the first vibration sensor 31 is Az. The vibration in the direction X perpendicular to the bridge axis detected by the second vibration sensor 32 is defined as Bx. Let the vibration in the vertical direction Z detected by the second vibration sensor 32 be Bz. Let Gx be the vibration in the direction perpendicular to the bridge axis X estimated for the riverbed R2a. Let Gz be the vibration in the vertical direction Z estimated for the riverbed R2a.
Of the vibration Ax in the direction X perpendicular to the bridge axis, the component caused by the primary vibration of the pier B1 (vibration of the pier B1 itself) is assumed to be Asx. Of the vibration Bx in the direction X perpendicular to the bridge axis, the component due to the primary vibration of the pier B1 is Bsx. Of the vibration Az in the vertical direction Z, the component due to the primary vibration of the pier B1 is Asz. Of the vibration Bz in the vertical direction Z, the component due to the primary vibration of the pier B1 is defined as Bsz.
For example, the unit of vibration Ax is m, and vibration Ax can be expressed as Ax (t) as a function of time t (seconds).

At this time, the vibrations Az and Bz can be approximated as shown in equations (7) and (8).
Az = Asz + Gz (7)
Bz = Bsz + Gz (8)
Further, the equation (9) is derived from the geometric relationship between the inclinations a and b.
Asz = (− a / b) · Bsz (9)
From (7) to (9),
Asz = Az-Gz
= Az- (Bz-Bsz)
= Az-Bz- (b / a) .Asz (10)

Therefore, equation (11) is obtained.
Asz = {a / (a + b)} (Az−Bz) (11)
By obtaining the difference between the vibration Az and the vibration Bz, the vibration of the pier B1 itself excluding the influence of the vibration of the riverbed R2a can be obtained.
Equation (12) is derived from the geometric relationship between the vibration Asx and the vibration Asz.
Asx = (1 / a) · Asz (12)
Substituting equation (11) for the right side of equation (12) leads to equation (13).
Asx = {1 / (a + b)} (Az−Bz) (13)

Further, the vibration Ax can be approximated as shown in Equation (14).
Ax = Asx + Gx (14)
Expression (15) is obtained from Expression (14) and Expression (13).
Gx = Ax-Asx
= Ax- (Az-Bz) / (a + b) (15)
Substituting Equations (3) and (4) into Equation (15) leads to Equation (16).
Gx = Ax− (Az−Bz) / (tan α + tan β) (16)

Next, the operation of the present detection device 2 configured as described above will be described. FIG. 8 is a flowchart showing the detection method S21 in the second embodiment of the present invention. When the detection apparatus 2 is activated, the arithmetic circuit 18 of the control unit 16 reads a program stored in the memory 37.
First, the initial natural frequency specifying step S6 (see FIG. 8) described above is performed, and an initial natural frequency ω ₀ that is an initial natural frequency of the pier B1 is obtained in advance. For example, assume that the initial natural frequency ω ₀ is determined to be 17 Hz. The user inputs this initial natural frequency ω ₀ from the input unit 20 and stores it in the memory 37 of the control unit 16.

Next, in the sensor mounting step (step S26), the user attaches the vibration sensors 31 and 32 to the upper surface B1a of the pier B1.
Next, in the support body vibration calculation step (step S28), the calculation circuit 18 of the control unit 36 detects the vibrations Ax, Az, Bx, Bz at the first time by the vibration sensors 31, 32, and the first of the pier B1. The vibration Gx in the direction X perpendicular to the bridge axis at one time is obtained by the equation (16). The vibration Bx may not be detected. Since the pier B1 vibrates around the lower part of the pier B1, the amplitude of the upper surface B1a is the largest among the vibration amplitudes of the pier B1. For this reason, vibration is more reliably detected by the vibration sensors 31 and 32.

The arithmetic circuit 18 performs fast Fourier transform on the vibration in the direction perpendicular to the bridge axis X measured by the first vibration sensor 31 to obtain a Fourier spectrum of the vibration. The Fourier spectrum obtained at this time is, for example, as shown in FIG. FIG. 9 shows the results of experiments to be described later. The horizontal axis in FIG. 9 represents the frequency (Hz), and the vertical axis represents the acceleration spectrum (gal · s). 1 gal is 0.01 m / s ² . In the Fourier spectrum of the vibration in FIG. 9, many peaks other than the natural frequency are dominant, and it is difficult to specify the peak value of the acceleration spectrum that is close to the initial natural frequency ω ₀ of 17 Hz.

Next, in the natural frequency specifying step (step S30), in the relationship of the phase difference between the vibration Ax and the vibration Gx with respect to the frequency, the phase difference is within a frequency range where the phase difference changes from 0 radians to π radians. The initial natural frequency among the frequencies when the phase difference is -π / 2 radians in the range of the frequency when the phase difference changes from 0 radians to -π radians when the frequency becomes π / 2 radians. The frequency closest to ω ₀ is defined as the natural frequency of the pier B1 at the first time.
Generally, the phase difference between the vibration in the bridge axis perpendicular direction X of the pier B1 and the vibration in the bridge axis perpendicular direction X of the riverbed R2a is π / 2 radians or −π / 2 at a frequency near the natural frequency of the pier B1. Become radians.

FIG. 10 shows the relationship of the phase difference between the vibration Ax and the vibration Gx with respect to the frequency. The horizontal axis in FIG. 10 represents the frequency (Hz), and the vertical axis represents the phase difference (radian).
Since the frequency when the phase difference closest to the initial natural frequency ω ₀ of 17 Hz is ± π / 2 radians is about 17.0 Hz, this frequency is set to the pier B1 at the first time. The natural frequency ω _{1 is} assumed. That is, the natural frequency ω _{1 at} the first time is not changed from the initial natural frequency ω _0, and it is evaluated that the soundness of the pier B1 is not changed between the initial state and the state at the first time.
In this case, since there is no change in the natural frequency, it is determined that no scouring S has occurred.

Above, all the processes of this detection method S21 are complete | finished. Thus, the natural frequency of the pier B1 is the initial natural frequency ω ₀ , and the natural frequency ω ₁ at the _first time and the change of the natural frequency of the pier B1 with time are detected.

If necessary, after the sensor mounting step S26, the support body vibration calculating step S28 and the natural frequency specifying step S30 may be performed a plurality of times. That is, in the vibration detection step S28, vibrations Ax, Az, Bx, and Bz at a second time after the first time are detected, and the vibration Gx in the direction X perpendicular to the bridge axis is obtained. In the natural frequency specifying step S30, the natural frequency of the pier B1 at the second time is calculated. By performing steps S28 and S30 a plurality of times, the natural frequency of the pier B1 at the third time, the fourth time,... After the second time is calculated.
By performing this detection method S21 in this way, the natural frequency of the pier B1 is continuously detected a plurality of times.

Next, the results of experiments using the model pier B1 will be described.
In the model pier B1, an experiment was conducted by attaching an auxiliary vibration sensor as an acceleration sensor to the ground below the pier B1. In this experiment, the distance h described above was 0.29 m, and the value of (ah + bh), which is the distance between the vibration sensors 31 and 32, was 0.25 m. In this case, the value of (a + b) is 0.86 from the equation (17).
0.25 / 0.29 = 0.86 (17)
The phase difference between the vibration in the direction perpendicular to the bridge axis X measured by the first vibration sensor 31 and the vibration in the direction perpendicular to the bridge axis X measured by the auxiliary vibration sensor is as shown in FIG. The horizontal axis in FIG. 11 represents the frequency (Hz), and the vertical axis represents the phase difference (radian). From the frequency at which the phase difference is ± π / 2 radians, it can be seen that the natural frequency is around 17 Hz.

In a state where the natural frequency of the model pier B1 is known (known), band pass filter processing was performed at a frequency near the natural frequency, and a Lissajous curve was drawn as shown in FIGS. FIG. 12 shows the detection result of the first vibration sensor 31 on the upstream side of the river flow. The horizontal axis represents acceleration (gal) in the direction X perpendicular to the bridge axis, and the vertical axis represents acceleration (gal) in the vertical direction Z. When the acceleration in the direction perpendicular to the bridge axis X and the acceleration in the vertical direction Z were approximated by a straight line equation by the least square method, the equation of the straight line L6 was as shown in equation (18).
y = 0.05044x−0.2269 (18)
FIG. 13 shows the detection result of the second vibration sensor 32 on the downstream side of the river flow. The horizontal axis represents acceleration (gal) in the direction X perpendicular to the bridge axis, and the vertical axis represents acceleration (gal) in the vertical direction Z. When the acceleration in the direction perpendicular to the bridge axis X and the acceleration in the vertical direction Z are approximated by a straight line equation by the least square method, the equation of the straight line L7 is as shown in equation (19).
y = −0.372x−0.3158 (19)

That is, the slope a in FIG. 7 is 0.5044 and the slope b is 0.372. In this case, the value of (a + b) was 0.87, which almost coincided with the value of equation (17).
Using this experimental condition, a solid line curve L9 representing the vibration Gx in the bridge axis perpendicular direction X as an estimated value in FIG. 14 and a dotted line curve representing the vibration in the bridge axis perpendicular direction X by the actually measured auxiliary vibration sensor. L10. The horizontal axis in FIG. 14 represents the frequency (Hz), and the vertical axis represents the acceleration spectrum (gal · s). FIG. 14 shows that the estimated ground vibration and the actually measured ground vibration are in good agreement. FIG. 15 shows the phase difference between the vibration Gx, which is an estimated value, and the vibration actually measured. The horizontal axis in FIG. 15 represents the frequency (Hz), and the vertical axis represents the phase difference (radian). The phase difference is close to 0 regardless of the frequency (Hz), and it can be seen that the estimated ground vibration and the actually measured ground vibration are in good agreement.

  From this, the frequency band necessary for the purpose of obtaining the natural frequency due to the primary vibration of the pier B1 is assumed as “the vibration of the pier B1 is a component of the primary vibration of the pier B1 and the vibration of the ground. It can be seen that the assumptions of the expressions (7) and (8), which are approximated to the sum of the above, are valid.

In the conventional natural frequency detection method, the natural frequency of the pier B1 is determined only from FIG. 9 described above.
As existing knowledge, if not only the vibration of the pier is actually measured, but also the vibration of the ground is actually measured, for example, the vibration in the direction perpendicular to the bridge axis at the end of the upper surface of the pier and the bridge shaft of the ground It is known that the natural frequency can be a frequency in which the Fourier spectrum ratio of the difference from the vibration in the perpendicular direction is dominant.
FIG. 16 shows the Fourier amplitude of the Fourier spectrum obtained from the vibration in the direction perpendicular to the bridge axis X at the end of the upper surface B1a of the pier B1 actually measured by the first vibration sensor 31 at the model pier B1, and the auxiliary vibration sensor. It is a figure which shows the relationship between the Fourier spectrum ratio which is a ratio with the Fourier amplitude of the Fourier spectrum obtained from the vibration of the bridge axis orthogonal direction X of the ground actually measured, and a frequency. The horizontal axis in FIG. 16 represents the frequency (Hz), and the vertical axis represents the Fourier spectral ratio (−). It can be seen that the Fourier spectrum ratio is excellent at the natural frequency ω _d of 17 Hz.
However, in an actual river, it is difficult to measure the vibration in the direction perpendicular to the bridge axis of the ground below the pier.

Instead of the actually measured vibration in the direction perpendicular to the bridge axis X of the ground, the Fourier spectrum ratio and the frequency obtained using the vibration Gx in the direction perpendicular to the bridge axis X of the riverbed R2a, which is the ground estimated by the above-described method, The relationship is shown in FIG. As in FIG. 16, it can be seen that the Fourier spectrum ratio is excellent at the natural frequency ω _d of 17 Hz. From FIG. 17, it is found that the frequency ω _e corresponding to the excellent Fourier spectrum ratio is 17 Hz, and this is the natural frequency of the pier B1.
Specifying the natural frequency using the Fourier spectrum ratio is easier than specifying the natural frequency according to FIG. 9 described above.
By confirming that the Fourier spectrum ratio is excellent at the vibration frequency when the phase difference is reversed, the specific accuracy of the natural frequency can be improved.

As described above, according to the detection device 2 and the detection method S21 of the present embodiment, the vibrations detected by the vibration sensors 31 and 32 are each affected by the vibration of the riverbed R2a that is the ground. For this reason, by calculating the difference between the vibrations of the vibration sensors 31 and 32, the vibration of the pier B1 itself in which the influence of the vibration of the riverbed R2a is suppressed can be obtained.
The phase difference at the first time is obtained, and the frequency at which this phase difference is ± π / 2 radians is set as the natural frequency of the pier B1. As a result, the natural frequency of the pier B1 at the first time can be reliably identified, and a change with time of the natural frequency of the pier B1 can be detected more reliably.

The vibration sensors 31 and 32 are attached to the upper surface B1a of the pier B1. Since the pier B1 vibrates around the lower part of the pier B1, the vibration amplitude of the pier B1 is the largest on the upper surface B1a. For this reason, vibration can be detected more reliably by the vibration sensors 31 and 32.
By performing the support body vibration calculating step S28 and the natural frequency specifying step S30 as a set a plurality of times, the natural frequency of the pier B1 can be continuously detected a plurality of times.

As mentioned above, although 1st Embodiment and 2nd Embodiment of this invention were explained in full detail with reference to drawings, the concrete structure is not restricted to this embodiment, The structure of the range which does not deviate from the summary of this invention Changes, combinations, deletions, etc. are also included. Furthermore, it goes without saying that the configurations shown in the embodiments can be used in appropriate combinations.
For example, in the first embodiment, the vibration sensor 11 may be attached not to the upper surface B1a of the pier B1 but to an intermediate portion in the vertical direction Z of the pier B1. The same applies to the vibration sensors 31 and 32.
The support may be a foundation such as ground or concrete, not the riverbed R2a.
Although the bridge B is a railway bridge, the bridge may be a road bridge or the like. The structure is not limited to the pier B1, and may be the bridge B itself or a building.

1, 2 Detector (Equipment frequency detector for bridge pier)
11 Vibration sensor 31 First vibration sensor 32 Second vibration sensor B1 Bridge pier (structure)
B1a Upper surface C Rotation center L1, L2 Line R2a River bottom (support)
S1 and S21 detection method (bridge natural frequency detection method)
S8 Vibration detection process S10 Coherence calculation process S12, S30 Natural frequency identification process S28 Support body vibration calculation process X Bridge axis perpendicular direction (horizontal direction)
Z Vertical direction ω ₀ Initial natural frequency

Claims (8)

A method for detecting the natural frequency of a structure for detecting the natural frequency of a structure disposed on a support,
Obtaining an initial natural frequency which is an initial natural frequency of the structure;
A vibration detection step of detecting horizontal vibration and vertical vibration along a horizontal plane at a first time by a vibration sensor attached above the support in the structure;
A coherence calculation step for obtaining a change in a coherence function depending on the frequency, using the horizontal vibration and the vertical vibration as inputs,
A natural frequency specifying step in which the frequency corresponding to the peak value of the coherence function closest to the initial natural frequency is the natural frequency of the structure at the first time;
A method for detecting the natural frequency of a structure, characterized in that:   The method for detecting a natural frequency of a structure according to claim 1, wherein the vibration sensor is attached to an end portion of an upper surface of the structure.   The method for detecting the natural frequency of a structure according to claim 1, wherein the vibration detecting step, the coherence calculating step, and the natural frequency specifying step are performed a plurality of times. A method for detecting the natural frequency of a structure for detecting the natural frequency of a structure disposed on a support,
Obtaining an initial natural frequency which is an initial natural frequency of the structure;
A first vibration sensor and a second vibration sensor are attached above the support in the structure,
An angle between a line connecting a position where the first vibration sensor is attached to the structure and a rotation center of the structure and a vertical direction is α, and a position where the second vibration sensor is attached to the structure; The angle between the line connecting the rotation center and the vertical direction is β, the vibration at the first time in the horizontal direction along the horizontal plane detected by the first vibration sensor is Ax, and the first vibration sensor detects When the vibration at the first time in the vertical direction is Az and the vibration at the first time in the vertical direction detected by the second vibration sensor is Bz,
A support body vibration calculation step of obtaining the horizontal vibration Gx of the support body at the first time by the equation (1);
In the relationship of the phase difference between the vibration Ax and the vibration Gx with respect to the frequency, the frequency when the phase difference is π / 2 radians within a range where the phase difference changes from 0 radians to π radians, and the order The frequency closest to the initial natural frequency among the frequencies when the phase difference is −π / 2 radians within a range in which the phase difference changes from 0 radians to −π radians, A natural frequency specifying step of setting the natural frequency of the structure at time;
A method for detecting the natural frequency of a structure, characterized in that:
Gx = Ax− (Az−Bz) / (tan α + tan β) (1)   The method according to claim 4, wherein the first vibration sensor and the second vibration sensor are attached to an upper surface of the structure.   6. The method for detecting the natural frequency of a structure according to claim 4, wherein the support vibration calculation step and the natural frequency specifying step are performed a plurality of times as a set. A natural frequency detector for a structure for detecting a natural frequency of a structure disposed on a support,
A vibration sensor mounted above the support in the structure;
A control unit that calculates the natural frequency of the structure based on the detection result of the vibration sensor;
With
The controller is
Using the vibration in the horizontal direction and the vibration in the vertical direction along the horizontal plane detected at the first time by the vibration sensor as inputs, the change in the coherence function according to the frequency is obtained,
The frequency corresponding to the peak value of the coherence function closest to the initial natural frequency of the structure determined in advance is set as the natural frequency of the structure at the first time. A natural frequency detector for a structure. A natural frequency detector for a structure for detecting a natural frequency of a structure disposed on a support,
A first vibration sensor and a second vibration sensor attached above the support in the structure;
A control unit that calculates a natural frequency of the structure based on detection results of the first vibration sensor and the second vibration sensor;
With
An angle between a line connecting a position where the first vibration sensor is attached to the structure and a rotation center of the structure and a vertical direction is α, and a position where the second vibration sensor is attached to the structure; When the angle between the line connecting the rotation center and the vertical direction is β,
The controller is
The horizontal vibration Ax along the horizontal plane detected by the first vibration sensor at the first time, the vertical vibration Az, and the second vibration sensor detected at the first time. From the vertical vibration Bz, the horizontal vibration Gx of the support at the first time is determined by the equation (2),
In the relationship of the phase difference between the vibration Ax and the vibration Gx with respect to the frequency, the frequency when the phase difference is π / 2 radians within a range where the phase difference changes from 0 radians to π radians, and the order Among the frequencies when the phase difference is −π / 2 radians in a range where the phase difference changes from 0 radians to −π radians, the value is closest to the initial natural frequency of the structure obtained in advance. The structure natural frequency detection device according to claim 1, wherein the vibration frequency is a natural frequency of the structure at the first time.
Gx = Ax− (Az−Bz) / (tan α + tan β) (2)

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