JPH0559312B2 - - Google Patents

Description

[Detailed description of the invention]

(Industrial Application Field) The present invention relates to a vibration damping method for suppressing vibrations in a piping system using a dynamic vibration absorber. (Prior art) In general, piping systems that are essential for the transfer of gases and liquids are more flexible and flexible than other structures because they have the flexibility to expand and contract in response to thermal expansion. It is easily affected by vibrations and causes problems such as fatigue damage and vibration noise due to resonance, and in order to prevent this, conventional methods have been used to suppress key points with support metal fittings. In addition, the seismic design of piping systems is important to ensure the safety of nuclear power plants. The earthquake resistance of the piping system is achieved by setting an excessively large number or by using a larger number of support fittings than necessary. (Problem to be Solved by the Invention) There is a need to support piping structures such as those described above with support fittings to prevent fatigue damage and vibration noise caused by resonance, and to improve the seismic design of nuclear power plants. If safety is to be ensured, the placement of the piping system will be restricted by the installation of support metal fittings, and seismic motion will be transmitted to the piping system via the support metal fittings, so It is hoped that an earthquake-resistant structure for piping systems, that is, a vibration damping method that does not rely on metal fittings, will emerge. Further, a typical piping system is a multi-degree-of-freedom system having a plurality of resonance peaks that should be suppressed and exhibits complex vibration behavior. For this reason, even if the piping system is held using a support fitting, it is unclear which part of the piping system should be supported to effectively control vibration. On the other hand, the inventor has proposed a theory for damping vibrations in multi-degree-of-freedom systems using dynamic vibration absorbers, and has shown the possibility of application to damping beam structures, Γ-shaped structures, flat plate structures, etc. This vibration damping method for a multi-degree-of-freedom system using a dynamic vibration absorber organically combines the modal analysis method and the design method of a dynamic vibration absorber. Since it can be treated as a set of 1-degree-of-freedom systems, we can use the established dynamic vibration absorber design method for damping a 1-degree-of-freedom system to create a dynamic damper for damping a multi-degree-of-freedom system in mode coordinates. All you need to do is design a vibration absorber, but the mode coordinates are virtual, and dynamic vibration absorbers are designed using physical coordinates. The installation location of the dynamic vibration absorber is determined from the mode shape, and the equivalent mass at that location (the equivalent mass of a 1-degree-of-freedom system for each mode) is identified as a physical quantity, and the dynamic vibration absorber is optimally designed for each mode. It is something to do. Therefore, in view of the above circumstances, the present invention applies the vibration damping method described above to the piping system, and uses a dynamic vibration absorber to improve the vibration damping and seismic safety of the piping system by using only the dynamic vibration absorber. It is an object of the present invention to provide a piping system vibration damping method (means for solving the problem) In order to achieve the above object, the piping system vibration damping method of the present invention is divided into pipe elements and coordinate transformation elements, and a mode analysis is performed for each element to determine the transfer matrix and state vector of the nodes between each element in three-dimensional space.The resonance peak is determined by frequency response analysis. , find the natural frequency and corresponding vibration mode shape at each resonance peak, identify the location where the maximum amplitude occurs for each mode, and set the location where the maximum amplitude occurs as the installation location of the dynamic vibration reducer. At the same time, find the equivalent mass of each dynamic vibration absorber installation location, find the equivalent spring constant of each mode from the above equivalent mass and natural frequency, and calculate the dynamic vibration of each mode based on these equivalent masses, equivalent spring constants, etc. The specifications of the vibration absorber, such as the mass, spring constant, and damping coefficient, are determined, and a dynamic vibration absorber is designed for each mode in accordance with the specifications, and is installed at the installation location. (Function) In the piping system vibration damping method using a dynamic vibration reducer as described above, a mode analysis is performed to determine the transfer matrix and state vector of the piping system, and each mode is determined from the vibration mode shape at each resonance peak in frequency response analysis. In addition to setting the location where the maximum amplitude occurs for each mode as the installation location of the dynamic damping amplitude, the mass, spring constant, damping coefficient, etc. of the dynamic vibration absorber for each mode are determined based on the equivalent mass and equivalent spring constant of that location. After determining the specifications, a dynamic vibration absorber designed for each mode is installed at the installation location, and this dynamic vibration absorber effectively damps the vibration of the piping system. The piping system is damped by a chisel without the need for supporting metal fittings, and seismic safety is improved. (Example) Examples of the present invention will be described below with reference to the drawings. In this example, we analyzed the vibration mode shapes of a piping system in a three-dimensional model, identified the equivalent mass of each mode, installed an optimally designed dynamic vibration absorber at a predetermined position of this piping system, and controlled it. Using a three-dimensionally expanded transfer matrix to study the sex vibration effect, 100
This study shows that three resonance peaks within Hz can be effectively suppressed by three double dynamic vibration absorbers, and the analytical results are verified through experiments. As shown in FIG. 1, the piping model of this embodiment is a copper pipe 1 having an outer diameter of 25 mm and an inner diameter of 15 mm, bent into four stages and fixed at both ends to a wall. Its shape is such that the first part 1a extends from one fixed end in the y direction.
Extends 300mm, and bends the second part 1b in the z direction to 480mm.
Stretch, and the third part 1c bends in the y direction to 140mm.
After stretching, the fourth part 1d bends in the x direction and extends by 600 mm, and then the fifth part 1e bends and extends in the y direction, with its ends fixed, and the parts other than both ends are not fixed. It is. Next, in order to analyze the vibration of the piping model in Fig. 1 using the transfer matrix method and obtain the vibration mode shape, 21 pipe elements 2 ₁ to 21 as shown in Fig. 2 are analyzed.
₂₂₁ and four coordinate transformation elements ₃₁ to ₃₄ .
Regarding the two basic elements 2 and 3 as above, 3
Find and analyze the transfer matrix in dimensional space. First, the transfer matrix of the pipe element 2 is determined. FIG. 3 shows the definition of variables and coordinates of the pipe element 2 placed between ends a and b in the three-dimensional space. Since the pipe element 2 can be considered as a beam element, if the bending, torsion, and axial transfer matrices related to the beam are combined, it can be expressed by a transfer matrix such as equation (1) or (1)'.

[Table] 〓 1 〓 _a 〓 ○ ○ ○
○ 1〓 _a 〓 1 〓 _b

{Z} _a = [B] _a・[Z] _b ...(1)' Where, X: Axial displacement, N: Axial force, θ: Torsion angle, T: Torque, Y: Lateral deflection, φ: Deflection angle, M: bending moment, F: shearing force. Subscripts y and x indicate the y-direction and x-direction components. In addition, [L], [M], [P] _y , and [P] _x indicate partial transmission matrices in the axial direction, torsional direction, and bending direction, and f _y and f _x act in the y direction and x direction, respectively. Define it as an external force term. Note that ○ indicates a zero matrix. The above [L] and [M] consist of the elements of the following formulas (2) and (3).

[Table] Here, σl=ω√ _{b b} and τl=ω√ _{t t} are defined. However, m _b and J _t represent the mass and moment of inertia of the pipe element 2, k _b and k _t represent the spring constants of the pipe element 2 in the axial direction and torsional direction, and ω is the angular frequency. Note that [P] _y and [P] _x are 4 whose elements are transcendental functions.
Although it is a ×4 matrix, the details are omitted here. Next, the transfer matrix of the coordinate transformation element 3 is determined. As shown in FIG. 4, there are three types of coordinate transformation in the orthogonal coordinate system: around the x-axis, y-axis, and z-axis. The rotation angles are defined as α, β, and γ, with clockwise rotation as a positive sign. Furthermore, Fig. 5 shows the two pipe elements 2 and 2 when rotated by α around the x-axis.
The definition of variables and coordinates between terminals a and b of 2 is shown, and based on this figure, the transfer matrix of coordinate transformation element 3 is expressed as in equation (4). {Z} _a = [T] _a・{Z} _b ……(4) However,

[Table] 〓 0 0 0 0 0
0 0 0 0 0 0
0 1 〓 _a
Here, C=cosα and S=sinα. Similarly, transfer matrices around the y-axis and z-axis are obtained. Based on the pipe element 2 and coordinate transformation element 3 obtained as described above, the definition of the transfer matrix and state vector of each element is shown in FIG. Here,
[B] _i is the transfer matrix of the i-th pipe element 2,
[T] _j indicates the j-th coordinate transformation matrix,
{Z} _k represents the state vector of node k. In addition,
{Z} ₁ and {Z} ₂₆ are the state vectors of both terminals,
In this case, both ends are fixed, so the following equations (5) and (6) are obtained. {Z} ₁ = {0N0T00M _y F _y 00M _x F _y 1} ^T ₁ ...(5) {Z} ₂₆ = {0N0T00M _y F _y 00M _x F _y 1} ^T ₂₆ ...(6) Next, the frequency Perform response analysis. When the transfer matrix calculation is performed based on FIG. 6, the state vectors of each node are expressed as in equations (7) and (8). {Z} ₂₅ = [H] ₂₅・{Z} ₂₆ {Z} ₂₄ = [H] ₂₄・{Z} ₂₆ {Z} ₂₃ = [H] ₂₃・{Z) ₂₆ 〓 〓 {Z} ₂ = [ H] ₂・{Z} ₂₆ …(7) {Z} ₁ = [H] ₁・{Z} ₂₆ …(8) Here, [H] ₂₅ = [B] ₂₁ [H] ₂₄ = [ B] ₂₀・[H] ₂₅ [H] ₂₃ = [T] ₄・[H] ₂₄ 〓 〓 [H] ₂ = [B] ₂・[H] ₃ [H] ₁ = [B] ₁ [H) ₂ , and therefore, if [Z] ₂₆ is known, all state vectors are calculated by the above equation (7), but as seen in equation (6), six unknown Contains variables. However, these unknown variables are
It can be solved using (5), (6) and equation (8), so equation
Calculation (7) becomes possible. In Figure 7, vibration is applied in the vertical direction at node k=7,
An example of compliance obtained at node k=11 is shown, and it can be seen that four resonance peaks are included in the range of 0 to 150 Hz. Also, the next resonance peak is about to appear around 150Hz. In this embodiment, three resonance peaks within 100 Hz are controlled. First, a vibration mode analysis is performed, and in order to control resonance peaks up to the third order, it is necessary to know the first to third order vibration mode shapes. 8 to 10 show their natural frequencies and corresponding vibration mode shapes. These vibration modes are shown in three-dimensional diagrams, front and side views, and from these diagrams, the locations 4 ₁ to 4 ₃ where the maximum amplitude occurs for each mode are as follows: The primary mode is located in the y-axis direction of node 12 ( 4 ₁ ), the secondary mode is in the z-axis direction of node 16 (4 ₂ ), and the tertiary mode is in the x-axis direction of node 6 (4 ₃ ). Next, find the installation location of the dynamic vibration absorbers and the equivalent mass at that location.Since the installation locations of the dynamic vibration absorbers 5 ₁ to 5 ₃ are the points where the maximum amplitude of each mode occurs, the above-mentioned locations 4 ₁ to 4 are determined. ₃ is defined as the installation location of the dynamic vibration absorbers 5 ₁ to 5 ₃ , and the setting locations and directions for each mode are shown in FIGS. 8 to 10. Furthermore, these locations are close to nodes of other modes, and the condition of non-coupling between each mode is also satisfied. In addition, each dynamic vibration absorber 5 ₁ to 5 ₃ was measured using the mass response method.
Installation location 4 ₁ to ₄ 3 primary to tertiary equivalent mass M ₁
〜M ₃ is calculated as follows. This mass sensitivity method is a method of determining the equivalent mass from the transition of the natural frequency that occurs when a known mass is added to the piping system. M ₁ = 1.42Kg M ₂ = 1.62Kg M ₃ = 1.31Kg Furthermore, from these equivalent masses and natural frequencies, the equivalent spring constants K ₁ to _{K 3} of each mode are also determined as follows. K ₁ = 5.35×10 ⁴ N/m K ₂ = 2.81×10 ⁵ N/m K ₃ = 4.23×10 ⁵ N/m Dynamic vibration absorbers 5 ₁ to 5 ₃ used in this example are single dynamic vibration absorbers. Three double dynamic vibration absorbers with superior vibration damping effect and vibration damping stability are used. FIG. 11 shows a mechanical model of the double dynamic vibration absorber 5i installed in the first degree of freedom system of the i-th mode. This double dynamic vibration absorber 5i has a first vibration absorbing part 5a and a second vibration absorbing part 5b in parallel, each having a mass, a spring, and a damper, where M _i , K _i
represents the equivalent mass and equivalent spring constant of the i-th mode, and (m _1i , k _1i , c _1i ) and (m _2i , k _2i , c _2i ) represent the first vibration absorption part for damping the i-th mode vibration. 5a and the second vibration absorbing part 5
The mass, spring constant, and damping coefficient of the damper of the vibration absorber in b are shown, respectively. As mentioned above, the equivalent mass M _i and spring constant K _i of each mode have been found, so if we set the mass ratio μ _i = m _i /M _i as a design parameter, we can use the already established design formula. Then, the specifications of each of the dynamic vibration reducers 5 ₁ to 5 ₃ are determined. m _1i = m _2i = μ _i M _i k _1i = m _1i (K _i /M _i ) × [0.403 (μ ₁ +0.13) ^-0.434 ] ² k _2i = m _2i (K _i /M _i ) × [ 1.04−0.72μ _i ] ² c _1i =2√ _{1i 1i} × [(μ _i /17.6) ^0.285 −0.065] c _2i =2√ _{2i 2i} × [(μ _i /3.06) ^0.377 −0.062] These specifications are satisfied The double dynamic vibration absorber exhibits the optimum vibration damping effect at a given mass ratio. This double dynamic vibration absorber has a spread of tuning points, so that even if the natural frequency of each mode fluctuates, the vibration absorbing part closest to the side that fluctuates works effectively, reducing the damping effect. It has a certain effect. Here, the following mass ratio μ _i is given for designing the first to third order dynamic vibration absorbers 5 ₁ to 5 ₃ . μ ₁ =0.05, η ₂ =0.05, μ ₃ =0.04 The specifications of the optimally designed double dynamic vibration absorber using these values are shown below. A 1st vibration absorption part 5a mode m(Kg) k(N/m) c(Ns/m) 1st order 0.071 1920 2.87 2nd order 0.081 10100 7.04 3rd order 0.052 12700 5.77 B 2nd vibration absorption part 5b mode m(Kg) k (N/m) c(Ns/m) 1st order 0.071 2690 4.14 2nd order 0.081 14100 10.16 3rd order 0.052 17200 8.00 To investigate the damping effect of dynamic vibration absorbers ₅₁ to ₅₃ designed as above, 3 A dimensionally expanded dynamic damper transfer matrix is required. The relationship between the transfer matrix D _r of the double dynamic vibration absorber and the state vector between the installed terminals a and b is expressed as follows. {Z} _a = [D] _r・{Z} _b = [D] _1r・[D] _2r・{
Z｝ _b
...(9) Here, subscripts 1r and 2r indicate the first vibration absorption part and the second vibration absorption part of the r-th mode. The transfer matrix of [D] _1r and [D] _2r has the same structure as Equation (1).
However, the partial transfer matrix used is replaced as follows. [L] = 1 −m _d ω ² 0 1 ...(10) [M] = 1 0 0 1 ...(11) [P] _x = [P] _y = 1 0 0 D _a 0 1 0 0 0 0 1 0 0 0 0 1 ...(12) This D _a is a different value depending on the mounting direction,
If the direction in which it acts as a dynamic vibration absorber is "1" and the direction orthogonal to it is "0", it is expressed as the following equation (13). D _a = ( _NR −jN _I /D −m _d ω ² ...“1” ...“0” ...(13) However, N _R = [ω _d ² (ω _d ² −ω ² ) + ( 2S _d ω _d ω) ² N _I = (2S _d ω _d ω ³ ) D = [(ωd ² −ω ² ) + (2S _d ω _d ω) ² ]/(−mω ² ) ...(14) Define, where m _d is the mass of the entire dynamic vibration absorber,
m, c, and k represent the mass, damping coefficient, and spring constant of the dynamic vibration absorber. To calculate the response after installing the dynamic vibration reducer, the above equation (9) can be substituted into the appropriate place in equation (7). The results of the vibration damping effect obtained by installing the dynamic vibration absorber as described above are shown in FIGS. 12 to 14. This figure shows 1
The compliance calculated in the y direction, z direction, and x direction for each of the nodes k = 11, 19, and 5 near the installation location of the next to third order dynamic vibration absorbers 5 ₁ to 5 ₃ is shown, and the broken line indicates the dynamic vibration absorber. The solid line shows the response before addition, and the solid line shows the response after adding the three double dynamic vibration absorbers 5 ₁ to 5 ₃ . It can be seen that each of the dynamic vibration absorbers 5 ₁ to 5 ₃ not only optimally suppresses the resonance peak of the mode that each of them shares, but also extends its effect to other locations. Note that the unsuppressed resonance peaks of the fourth order and above appear shifted to a somewhat lower frequency due to the effect of the addition of the dynamic vibration reducer. Next, an example of the double dynamic vibration absorber 10 embodying the dynamic model shown in FIG. 9 is shown in FIGS. 15 and 1.
It is shown in Figure 6. Two upper and lower leaf springs 14 made of phosphor bronze plates, one end of which is fixed to the support member 13, extend from both sides of the support member 13. Upper and lower leaf springs are provided at the left and right free ends of the leaf spring 14, respectively. Mass bodies 15a and 15b are sandwiched between 14 and 14, and these mass bodies 15a and 15b are made of copper and have an I-shaped cross section. Further, a pair of permanent magnets 17 are arranged on both sides of each mass body 15a, 15b at a constant interval. The permanent magnet 17 is attached to a case 16 made of aluminum. The support body 13 is fixedly attached to the pipe 1 at a predetermined installation location of the piping system, and mass bodies 15a and 15b are mounted on both sides of the support body 13, respectively, and plate springs 14 and 14 having a predetermined spring constant are mounted on both sides of the support body 13.
and a damper formed by permanent magnets 17, 17 for obtaining magnetic damping.
10b is configured. This dynamic vibration absorber 10 is
It utilizes the magnetic attenuation that occurs when the mass body 15 moves without mechanical contact in the magnetic field created by the pair of permanent magnets 17, and the mass body 15 also serves as a magnetic damper. The tuning point of the first and second vibration absorbers 10a, 10b in the dynamic vibration absorber 10i is adjusted by the mass ratio μ
The masses m ₁ and m ₂ of the mass bodies 15a and 15b corresponding to
settings, the leaf spring 14 corresponding to the spring constants k ₁ , k ₂ ,
The design can be changed by setting the lengths l ₁ and l ₂ of 14 and the spacing between the magnets 17 and 17 and the masses 15a and 15b corresponding to the damping coefficients c ₁ and c ₂ , and the design can be changed based on the values of the above specifications. Therefore, these values are set optimally. FIG. 17 shows the results of confirming the damping effect by installing three dynamic vibration reducers 10 as described above at locations designated by theoretical analysis. In this test, the experimental results obtained at the node k=11 in the y direction by vertically vibrating the node k=7 are shown. This corresponds to Fig. 12, but considering that in the experimental results, the resonance peak appears low due to the influence of masses other than the vibration absorber mass that constitutes the dynamic vibration absorber, it can be seen that both corresponds well,
The damping effect shown in theory could be confirmed through experiments. The damping effect brought about by the three double dynamic vibration absorbers 10 is also clearly recognized by the impulse response of the acceleration waveform shown in FIG. Note that the influence of the fourth-order or higher-order resonance peak that appears after damping can be easily removed by further installing a dynamic vibration absorber. Moreover, specific structural examples of other double dynamic vibration absorbers are shown in FIGS. 19 to 21. This double dynamic vibration absorber 20 is
It is attached so as to surround the outer periphery of the pipe 1 of the piping system, thereby simplifying the installation structure. The central support body 21 has a cubic shape, and has a mounting hole 21 a corresponding to the outer diameter of the pipe 1 penetratingly formed therein, and is divided into two parts to form a fastening flange 21 .
b is attached and is configured to clamp the pipe 1. A pair of leaf springs 22 are attached to extend parallel to the left and right from this support body 21.
Rectangular cylindrical mass bodies 23a, 23b are provided at the left and right ends of 2.
are connected, each mass body 23a, 23b is provided in a split structure, and is integrated at an outer fastening flange 23c. Furthermore, inner members 24, 24 are arranged inside the mass bodies 23a, 23b at a predetermined interval, and the inner members 24, 24 are fixed to the outer periphery of the pipe 1 and move together. It is constructed in such a way that it is divided into parts and holds the pipe 1 therebetween. The inner members 24, 24 and the mass bodies 23a, 23
A damper means 25 is installed between it and b. The damper means 25 is made of, for example, a viscoelastic body, and similarly to the magnetic damper of the above example, the mass body 23a is connected to the inner members 24, 24 fixed to the pipe 1 via the leaf springs 22, 22. ，
It is configured to give a predetermined damping characteristic to the movement of 23b. Further, the damper means 25 includes:
Mechanisms such as magnetic dampers and fluid dampers can be adopted. Due to the above structure, the left and right sides have different tuning characteristics.
A double dynamic vibration absorber 20 including second vibration absorbers 20a and 20b is configured. By installing the double dynamic vibration absorber 20 in this example so as to surround the outer periphery of the pipe 1, there are few protruding parts from the pipe 1, and space can be used effectively. The installation performance is good. According to the embodiment described above, the damping theory of a multi-degree-of-freedom system using a dynamic vibration absorber is applied to damping the piping system,
Using the transfer matrix method for three-dimensional vibration analysis of piping systems including dynamic vibration absorbers, the three resonance peaks can be optimally suppressed by three double dynamic vibration absorbers, and this theory is applicable to piping systems. This makes it possible to damp the vibrations of piping systems without using support fittings. Also,
If the mass ratio is used as a design parameter, it becomes possible to design a piping system with a dynamic vibration absorber that accurately estimates its seismic response. (Effects of the Invention) According to the present invention as described above, a mode analysis of the piping system is performed, and from the vibration mode shapes obtained by frequency response analysis, the location where the maximum amplitude occurs for each mode is determined as the installation location of the dynamic vibration absorber. The dynamic vibration absorber's mass, spring constant, damping coefficient, and other specifications are determined based on the equivalent mass and equivalent spring constant of the installation location, and the dynamic vibration absorber is designed for each mode accordingly. By installing the vibration absorber at the above-mentioned location, the vibration of the piping system can be effectively suppressed by this dynamic vibration absorber, and the vibration damping and earthquake resistance of the piping system can be achieved by using only the dynamic vibration absorber without any support metal fittings. This can improve safety.

[Brief explanation of the drawing]

FIG. 1 is a perspective view showing the piping model of the embodiment, FIG. 2 is a division diagram dividing the piping model into pipe elements and coordinate transformation elements, and FIG. 3 is an explanatory diagram showing the definition of variables and coordinates of the pipe elements. Figure 4 is an explanatory diagram showing the types of coordinate transformations, Figure 5 is an explanatory diagram showing the coordinate transformation around the x-axis and the definition of variables, Figure 6 is an illustration showing the transfer matrix display of the piping model, and Figure 7 is an explanatory diagram showing the types of coordinate transformations. Characteristic diagram showing an example of compliance of the piping model, Figure 8 is a schematic diagram showing the primary mode and the location where the dynamic vibration reducer is installed, Figure 9 is a schematic diagram showing the secondary mode and the location where the dynamic vibration reducer is installed, and Figure 10 is the diagram showing the location where the dynamic vibration absorber is installed. A schematic diagram showing the tertiary mode and the location of the dynamic vibration reducer, Figure 11 is a mechanical model diagram showing the damping model of the i-order mode using a double dynamic vibration absorber, and Figure 12
Figures 14 to 14 are characteristic diagrams showing compliance calculated at nodes near the installation locations of primary to tertiary dynamic vibration absorbers in comparison with the state before the dynamic vibration absorbers were installed.
The figure is a front view showing an example of the structure of a double dynamic vibration absorber.
The figure is a cross-sectional view taken along line A-A in Figure 15, Figure 17 is a measurement diagram showing the damping effect of the dynamic vibration absorber in an experimental example, and Figure 18 is the vibration damping effect due to acceleration response with and without the dynamic vibration absorber. Figure 19 is a front view showing the structure of another example of a double dynamic vibration absorber, Figure 20 is a measurement diagram for comparison.
The figure is a cross-sectional view taken along the line B--B in FIG. 19, and FIG. 21 is a cross-sectional view taken along the line C--C in the same figure. 1...Pipe (piping system), 2...Pipe element,
3... Coordinate conversion element, 4... Installation location, 5... Dynamic vibration absorber, 10, 20... Double dynamic vibration absorber, 13, 2
1... Support body, 14, 22... Leaf spring, 15, 2
3... Mass body, 17... Magnet, 25... Damper means.

Claims (1)

[Claims] 1. A piping system vibration damping method that uses a dynamic vibration absorber that dampens piping system vibration by installing a dynamic vibration absorber composed of a mass, a spring, a damper, etc. in the piping system. Divide the piping system into pipe elements and coordinate transformation elements, perform modal analysis for each element to determine the transfer matrix and state vectors of nodes between each element in three-dimensional space, and determine resonance peaks by frequency response analysis. In addition, find the natural frequency and corresponding vibration mode shape at each resonance peak, identify the location where the maximum amplitude occurs for each mode, and select the location where the maximum amplitude occurs as the installation location of the dynamic vibration absorber. At the same time, find the equivalent mass of each dynamic vibration reducer installation location, then find the equivalent spring constant of each mode from the above equivalent mass and natural frequency, and set each mode based on these equivalent mass, equivalent spring constant, etc. Specifications such as mass, spring constant, damping coefficient, etc. of the dynamic vibration absorber are determined, and the dynamic vibration absorber is designed for each mode correspondingly and installed at the installation location. A method of damping piping systems using dynamic vibration absorbers.