CN109726521B - Method for eliminating suspension support influence in frequency response function aiming at free mode test - Google Patents

Abstract

The invention discloses a method for eliminating suspension support influence in a frequency response function aiming at free mode test, wherein in the free mode test, a tested structure is usually suspended and supported by adopting a soft rope or a soft spring and the like, and the free boundary condition is approximately simulated; however, the suspension support can introduce additional rigidity and damping to the test structure, and further bring a certain influence on the measured frequency response function; the invention relates to a method for eliminating suspension support influence in a frequency response function aiming at free modal test, which can eliminate the influence of suspension support rigidity and damping on the measured frequency response function and accurately acquire the frequency response function of a free structure by measuring the frequency response function related to a suspension point under the condition of giving the support rigidity and the support damping.

Description

Method for Eliminating Suspension Support Effects in Frequency Response Functions for Free Mode Testing

technical field

The invention belongs to the technical field of modal testing, and relates to a method for correcting frequency response function data, in particular to a method for eliminating the influence of suspension supports in frequency response functions for free modal tests, where the influence of suspension supports mainly refers to the stiffness of suspension supports and the additional effect of damping on the frequency response function.

Background technique

Free modal test is a relatively common type of modal test, which aims to obtain the dynamic characteristics of free structures. In this type of test, the structure under test should be in a free state similar to "suspension". However, in practice, this state is difficult to achieve. Usually, soft ropes or soft springs are used to suspend and support the structure under test to approximate free boundary conditions. Obviously, the suspension support will introduce additional stiffness and damping to the test structure, which will affect the test results to a certain extent, and the most direct impact is the measured frequency response function.

Contents of the invention

In order to solve the above technical problems, the present invention discloses a method for eliminating the influence of suspension support in the frequency response function for free mode testing.

The technical solution adopted in the present invention is: a method for eliminating the influence of the suspension support in the frequency response function for the free mode test, which is characterized in that: for the single-point suspension, it is assumed that the self-stiffness of the structure C is small enough to ignore the suspension support The structure C is suspended at point s, the suspension support effect is equivalent to a spring with a stiffness of k _s and a damper with a size of c _s , point p is the excitation point, and point l is the measurement point, where "point p" and " Point l" is any two points on the structure; in order to eliminate the influence of suspension support, a "virtual support" is applied at point s, and the "negative stiffness" k′ _s = -k _s and "negative damping" c in the "virtual support" ′ _s = -c _s offsets the influence of the suspension support, making the structure equivalent to a free state;

For the convenience of analysis, point s is split into two points, s and s′, and in the “virtual support”, point s is expressed by point s′;

Assuming that the suspended structure C is substructure I, and the "virtual support" is substructure II, the combination of substructure I and substructure II results in a free structure;

Analyze substructures I and II separately;

For substructure Ⅰ, the relationship between the output displacement response and the input force in the frequency domain is established,

表示悬挂状态下l、s点之间的位移频响函数；

表示悬挂状态下s、p点之间的位移频响函数；

表示悬挂状态下s点处的原点位移频响函数；Among them, X _l and X _s represent the displacement response of substructure I at points l and s, respectively, and F _p and R _s represent the forces on substructure I at points p and s, respectively;

Indicates the displacement frequency response function between points l and s in the suspended state;

Indicates the displacement frequency response function between points s and p in the suspended state;

Indicates the origin displacement frequency response function at point s in the suspended state;

For substructure II, the relationship between the output displacement response and the input force is also established,

X' _s = α _s's' R _s' (2)

In the formula,

Among them, X′ _s′ and R _s′ represent the displacement response and the acting force of substructure II at point s respectively; α _s′s′ represents the frequency response function of the origin displacement of substructure II at point s; jω where j is a complex unit, and ω is an independent variable of the frequency response function;

The constraint conditions of force and displacement at connection point s or s′ are respectively:

R _s +R _s′ = 0 (4)

X _s ＝X _s′ (5)

Simultaneous formulas (1)～(5), get

表示悬挂状态下l、p点位移频响函数；为了避免混淆，命名自由状态下的频响函数为“准确频响函数”，悬挂状态下的频响为“实测频响函数”，即α_lp为准确频响函数，

均为实测频响函数；In the formula, α _lp represents the displacement frequency response function of points l and p in the free state;

Indicates the displacement frequency response function of points l and p in the suspension state; in order to avoid confusion, the frequency response function in the free state is named "accurate frequency response function", and the frequency response in the suspension state is "measured frequency response function", that is, α _lp is the exact frequency response function,

Both are measured frequency response functions;

有所差异，而这种差异正是由于支承的刚度和阻尼导致；而且在悬挂刚度k_s和阻尼c_s给定的情况下，通过测量与悬挂点s相关的位移频响函数可计算得到准确频响函数α_lp，即达到消除位移频响函数

中支承影响的目的；According to formula (6), it can be seen that the exact frequency response function α _lp and the measured frequency response function

There is a difference, and this difference is caused by the stiffness and damping of the support; and when the suspension stiffness k _s and damping c _s are given, the exact frequency response function can be calculated by measuring the displacement frequency response function related to the suspension point s Frequency response function α _lp , that is, to achieve the elimination of displacement frequency response function

The purpose of supporting influence in the medium;

The above analyzes are all aimed at the displacement frequency response function, but in the actual measurement, acceleration sensors are mostly used, and the measured frequency response function is the acceleration frequency response function. For the case of acceleration frequency response, just multiply the left and right sides of formula (6) by -ω ² to get the relationship between acceleration frequency response and accurate acceleration frequency response (7)

表示悬挂状态下l、p点之间的加速度频响函数；

表示悬挂状态下s、p点之间的加速度频响函数；

表示悬挂状态下l、s点之间的加速度频响函数；

表示悬挂状态下s点加速度原点频响函数；只要支承刚度k_s和支承阻尼c_s大小已知，就能通过测量与悬挂点相关的频响函数来获取自由结构的频响函数A_lp。In the formula, A represents the acceleration frequency response function, and A _lp represents the acceleration frequency response function between points l and p of the free structure;

Indicates the acceleration frequency response function between points l and p in the suspended state;

Indicates the acceleration frequency response function between points s and p in the suspended state;

Indicates the acceleration frequency response function between points l and s in the suspended state;

Represents the frequency response function of the acceleration origin at point s in the suspension state; as long as the support stiffness k _s and support damping c _s are known, the frequency response function _Alp of the free structure can be obtained by measuring the frequency response function related to the suspension point.

For multi-point suspension, it is assumed that the self-stiffness of structure C is small enough to ignore the influence of suspension support, structure C is in a multi-point suspension state, and the suspension points are 1, 2, ..., n respectively; the support stiffness of each suspension point is k _i , the damping size is c _i , i=1, 2, ..., n; point p is the excitation point, point l is the measurement point, where "point p" and "point l" are any two points on the structure; for To eliminate the influence of the suspension support, apply a "virtual support" at each suspension point in turn, and the "negative stiffness" k′ _i = _-ki and "negative damping" c′ _i = _-ci in the "virtual support" are offset respectively The influence of each suspension support, so as to obtain the structure in a free state;

For the convenience of analysis, the suspension point s _i is split into two points s _i and s′ _i , and in the “virtual support”, s _i is used to express s _i ;

The original suspended structure C is regarded as substructure I, and the virtual support is regarded as substructure II, III, ...; for substructure I, the relationship between the output displacement response and the input force in the frequency domain is established,

Among them, k=1, 2, ..., n, X _l and X _k represent the displacement of substructure I at point l and point k respectively

和R_i分别表示子结构Ⅰ在p点、S_i点和i点所受的作用力；

表示悬挂状态下l、p点之间的位移频响函数；

表示悬挂状态下l、S_i点之间的位移频响函数；

表示悬挂状态下k、p点之间的位移频响函数；

表示悬挂状态下k、i点之间的位移频响函数；Response, F _p ,

and R _i denote the acting force on substructure I at point p, S _i and i, respectively;

Indicates the displacement frequency response function between points l and p in the suspended state;

Indicates the displacement frequency response function between points l and S _i in the suspended state;

Indicates the displacement frequency response function between points k and p in the suspension state;

Indicates the displacement frequency response function between points k and i in the suspended state;

For substructures II, III, ..., the relationship between the output displacement response and the input force is also established,

X′ _k ＝α′ _kk R′ _k (10)

In the formula,

Among them, X′ _k and R _k represent the displacement responses and _acting forces of substructures II, III, ... at point k, respectively; Origin displacement frequency response function; j in jω is a complex unit, and ω is an independent variable of frequency response function;

The constraint conditions of force and displacement at connection point s or s′ are respectively:

R _k + R′ _k = 0 (12)

X _k = X′ _k (13)

Simultaneous formula (8)～(13), get

α ^(s) F=X (14)

In the formula,

Solving formula (14), we get

表示悬挂结构体的位移频响函数；α′₁₁，α′₂₂……表示添加的虚拟支承分别在1、2……点处的原点位移频响函数；式(15)表明，对位移频响函数

修正需要额外测量与悬挂点1，2…n相关的多个位移频响函数，所需测量的位移频响函数数量随着悬挂点的增多而增加；In the formula, α _lp represents the displacement frequency response function between points l and p of the free structure;

Indicates the displacement frequency response function of the suspended structure; α′ ₁₁ , α′ ₂₂ ... represent the origin displacement frequency response function of the added virtual support at points 1, 2... respectively; Equation (15) shows that the displacement frequency response function

The correction requires additional measurement of multiple displacement frequency response functions related to suspension points 1, 2...n, and the number of displacement frequency response functions required to be measured increases with the number of suspension points;

需要额外测量(N²+5N)/2组位移频响函数，分别为原点位移频响函数

和跨点位移频响函数

这些位移频响函数均与悬挂点相关；以上结论是针对激励点p、响应点l和悬挂点1，2…n均不重合的情况，当它们其中某些点重合时，式(15)会适当简化，修正工作中所需测量的位移频响函数也会适当减少；It is deduced from formula (15), for the case of N-point suspension, the correction

Additional measurements (N ² +5N)/2 sets of displacement frequency response functions are required, which are the origin displacement frequency response functions

and across point displacement frequency response function

These displacement frequency response functions are all related to the suspension point; the above conclusion is for the case that the excitation point p, the response point l and the suspension point 1, 2...n do not overlap. When some of them overlap, the formula (15) will be Appropriate simplification, the displacement frequency response function that needs to be measured in the correction work will also be appropriately reduced;

For the case of acceleration frequency response, it is only necessary to multiply both ends of formula (15) by -ω ² to obtain the expression form of the acceleration frequency response function A,

表示悬挂状态下l、p点之间的加速度频响函数；

表示悬挂状态下n点加速度原点频响函数；A′₁₁，A′₂₂……A′_nn分别表示添加的虚拟支承在1、2……n点处的加速度频响函数。In the formula, A represents the acceleration frequency response function, and A _lp represents the acceleration frequency response function between points l and p of the free structure;

Indicates the acceleration frequency response function between points l and p in the suspended state;

Indicates the frequency response function of the acceleration origin of point n in the suspension state; A′ ₁₁ , A′ ₂₂ ... A' _nn represent the acceleration frequency response function of the added virtual support at points 1, 2...n, respectively.

The invention relates to a method for eliminating the influence of the suspension support in the frequency response function for the free mode test. Under the condition of given support stiffness and support damping, the method can eliminate the suspension support by measuring the frequency response function related to the suspension point. The influence of support stiffness and damping on the measured frequency response function, to accurately obtain the frequency response function of the free structure.

Description of drawings

Fig. 1 is the free mode test suspension support schematic diagram in the background technology of the present invention;

Fig. 2 is the structure free modal test schematic diagram (single-point suspension) of the embodiment of the present invention;

Fig. 3 is a schematic diagram of the conversion of a suspended structure into a free structure according to an embodiment of the present invention;

Fig. 4 is the schematic diagram of structure free modal test (multi-point suspension) of the embodiment of the present invention;

Fig. 5 is a schematic diagram of the transformation of a suspended structure into a free structure according to an embodiment of the present invention;

Fig. 6 is the free beam modal test schematic diagram of the embodiment of the present invention;

与准确频响函数A₂₄对比示意图；Fig. 7 is the frequency response function of the measurement of the embodiment of the present invention

Schematic diagram of comparison with the exact frequency response function A ₂₄ ;

与准确频响函数A₂₄对比示意图；Fig. 8 is the revised frequency response function of the embodiment of the present invention

Schematic diagram of comparison with the exact frequency response function A ₂₄ ;

(未消除支承阻尼)与准确频响函数A₂₄对比示意图。Fig. 9 is the revised frequency response function of the embodiment of the present invention

(without eliminating the support damping) and the accurate frequency response function A ₂₄ comparison diagram.

detailed description

In order to facilitate those of ordinary skill in the art to understand and implement the present invention, the present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the implementation examples described here are only used to illustrate and explain the present invention, and are not intended to limit this invention.

Please see Fig. 2, a method for eliminating the influence of suspension support in the frequency response function provided by the present invention for free mode testing, for single-point suspension, the structure C is suspended at point s, and the suspension support effect is equivalent to k _s stiffness A spring of size c _s and a damper of size c s. Point p is the excitation point, and point l is the measurement point. Assume that the self-stiffness of structure C is small enough to ignore the influence of suspension supports. In order to eliminate the influence of suspension support, a "virtual support" can be applied at point s, as shown in the dotted line box on the left in Figure 3. The “negative stiffness” (k′ _s =-k _s ) and “negative damping” (c′ _s =-c _s ) in the “virtual support” offset the influence of the suspension support, making the structure equivalent to the right side of Figure 3 free state. Point s and point s′ in the left figure of Figure 3 actually represent the same point, and are split into two points for the convenience of analysis.

Essentially, imposing "virtual support" on the original suspension structure C belongs to the category of structural modification, so the method of structural dynamic modification can be used for modeling. If the suspended structure C is regarded as substructure I, and the virtual support is regarded as substructure II, then the free structure on the right side of Figure 3 can be obtained by combining substructure I and substructure II. Substructures I and II were analyzed separately. For substructure I, the relationship between the output displacement response and the input force in the frequency domain can be established,

表示悬挂状态下l、s点之间的位移频响函数；

表示悬挂状态下s、p点之间的位移频响函数；

表示悬挂状态下s点处的原点位移频响函数；Among them, X _l and X _s represent the displacement response of substructure I at points l and s, respectively, and F _p and R _s represent the forces on substructure I at points p and s, respectively;

Indicates the displacement frequency response function between points l and s in the suspended state;

Indicates the displacement frequency response function between points s and p in the suspended state;

Indicates the origin displacement frequency response function at point s in the suspended state;

For substructure II, the relationship between the output displacement response and the input force is also established,

X' _s = α _s's' R _s' (2)

In the formula,

Among them, X′ _s′ and R _s′ represent the displacement response and the acting force of substructure II at point s respectively; α _s′s′ represents the frequency response function of the origin displacement of substructure II at point s; jω where j is a complex unit, and ω is an independent variable of the frequency response function;

The constraint conditions of force and displacement at connection point s or s′ are respectively

R _s +R _s′ = 0 (4)

X _s ＝X _s′ (5)

Simultaneous formulas (1)～(5), get

表示结构体在悬挂状态下l、p点之间的位移频响函数；为了避免混淆，命名自由状态下的频响函数为“准确频响函数”，悬挂状态下的频响函数为“实测频响函数”，即α_lp为准确频响函数，

均为实测频响函数；In the formula, α _lp represents the displacement frequency response function of points l and p in the free state;

Indicates the displacement frequency response function between points l and p of the structure in the suspension state; in order to avoid confusion, the frequency response function in the free state is named "accurate frequency response function", and the frequency response function in the suspension state is "measured frequency response function". Response function", that is, α _lp is the exact frequency response function,

Both are measured frequency response functions;

有所差异，而这种差异正是由于支承的刚度和阻尼导致；而且在悬挂刚度k_s和阻尼c_s给定的情况下，通过测量与悬挂点s相关的频响函数可计算得到准确频响函数α_lp，即达到消除频响函数

中支承影响的目的；According to formula (6), it can be seen that the exact frequency response function α _lp and the measured frequency response function

There is a difference, and this difference is caused by the stiffness and damping of the support; and when the suspension stiffness k _s and damping c _s are given, the exact frequency can be calculated by measuring the frequency response function related to the suspension point s Response function α _lp , that is, to eliminate the frequency response function

The purpose of supporting influence in the medium;

The above analyzes are all aimed at the displacement frequency response function, but in the actual measurement, acceleration sensors are mostly used, and the measured frequency response function is the acceleration frequency response function. For the case of acceleration frequency response, just multiply the left and right sides of formula (6) by -ω ² to get the relationship between acceleration frequency response and accurate acceleration frequency response (7)

表示悬挂状态下l、p点之间的加速度频响函数；

表示悬挂状态下s、p点之间的加速度频响函数；

表示悬挂状态下l、s点之间的加速度频响函数；

表示悬挂状态下s点加速度原点频响函数；只要支承刚度k_s和支承阻尼c_s大小已知，就能通过测量与悬挂点相关的频响函数来获取自由结构的频响函数A_lp。In the formula, A represents the acceleration frequency response function, and A _lp represents the acceleration frequency response function between points l and p of the free structure;

Indicates the acceleration frequency response function between points l and p in the suspended state;

Indicates the acceleration frequency response function between points s and p in the suspended state;

Indicates the acceleration frequency response function between points l and s in the suspended state;

Represents the frequency response function of the acceleration origin at point s in the suspension state; as long as the support stiffness k _s and support damping c _s are known, the frequency response function _Alp of the free structure can be obtained by measuring the frequency response function related to the suspension point.

Considering that in some cases it is necessary to carry out multi-point suspension on the structure under test, the method for eliminating the influence of support in the case of multi-point suspension is further deduced below, and the case of single-point support can be regarded as a special case of multi-point support here. For the case of multi-point suspension, the method of applying "negative stiffness" and "negative damping" can also be adopted to eliminate the support effect in the frequency response function.

Please see Figure 4, for multi-point suspension, it is assumed that the self-stiffness of structure C is small enough to ignore the influence of suspension support, structure C is in a multi-point suspension state, and the suspension points are 1, 2, ..., n; each The support stiffness of the suspension point is k _i , the damping size is c _i , i=1, 2, ..., n; point p is the excitation point, point l is the measurement point, where "point p" and "point l" are the points on the structure Any two points; in order to eliminate the influence of the suspension support, a "virtual support" is applied at each suspension point in turn (as shown in the part in the dotted line box on the left side of Figure 5), and the "negative stiffness"k' _i in the "virtual support" = -k _i and "negative damping"c' _i = -c _i respectively counteract the influence of each suspension support, so as to obtain the free state structure;

For the convenience of analysis, the suspension point s _i is split into two points s _i and s′ _i , and in the “virtual support”, s _i is used to express s _i ;

The process of adding virtual supports to the original suspension structure C can be regarded as the process of structural dynamics modification. If the original suspended structure C is regarded as substructure I, the virtual support inside the dotted line frame is regarded as substructure II, III.... For substructure I, the relationship between the output displacement response and the input force in the frequency domain can be established,

和R_i分别表示子结构Ⅰ在p点、S_i点和i点所受的作用力；

表示悬挂状态下l、p点之间的位移频响函数；

表示悬挂状态下l、S_i点之间的位移频响函数；

表示悬挂状态下k、p点之间的位移频响函数；

表示悬挂状态下k、i点之间的位移频响函数；Among them, k=1, 2,..., n, X _l and X _k represent the displacement response of substructure I at point l and point k respectively, F _p ,

and R _i denote the acting force on substructure I at point p, S _i and i, respectively;

Indicates the displacement frequency response function between points l and p in the suspended state;

Indicates the displacement frequency response function between points l and S _i in the suspended state;

Indicates the displacement frequency response function between points k and p in the suspension state;

Indicates the displacement frequency response function between points k and i in the suspended state;

For substructures II, III, ..., the relationship between the output displacement response and the input force is also established,

X′ _k ＝α′ _kk R′ _k (10)

In the formula,

Among them, X′ _k and R _k represent the displacement responses and _acting forces of substructures II, III, ... at point k, respectively; Origin displacement frequency response function; j in jω is a complex unit, and ω is an independent variable of frequency response function;

The constraint conditions of force and displacement at connection point s or s′ are respectively:

R _k + R′ _k = 0 (12)

X _k = X′ _k (13)

Simultaneous formula (8)～(13), get

α ^(s) F=X (14)

In the formula,

Solving formula (14), we get

表示悬挂结构体的位移频响函数；α′₁₁，α′₂₂……表示添加的虚拟支承分别在1、2……点处的原点位移频响函数；式(15)表明，对位移频响函数

修正需要额外测量与悬挂点1，2…n相关的多个位移频响函数，所需测量的位移频响函数数量随着悬挂点的增多而增加；In the formula, α _lp represents the displacement frequency response function between points l and p of the free structure;

Indicates the displacement frequency response function of the suspended structure; α′ ₁₁ , α′ ₂₂ ... represent the origin displacement frequency response function of the added virtual support at points 1, 2... respectively; Equation (15) shows that the displacement frequency response function

The correction requires additional measurement of multiple displacement frequency response functions related to suspension points 1, 2...n, and the number of displacement frequency response functions required to be measured increases with the number of suspension points;

需要额外测量(N²+5N)/2组位移频响函数，分别为原点位移频响函数

和跨点位移频响函数

这些位移频响函数均与悬挂点相关；以上结论是针对激励点p、响应点l和悬挂点1，2…n均不重合的情况，当它们其中某些点重合时，式(15)会适当简化，修正工作中所需测量的位移频响函数也会适当减少；It is deduced from formula (15), for the case of N-point suspension, the correction

Additional measurements (N ² +5N)/2 sets of displacement frequency response functions are required, which are the origin displacement frequency response functions

and across point displacement frequency response function

These displacement frequency response functions are all related to the suspension point; the above conclusion is for the case that the excitation point p, the response point l and the suspension point 1, 2...n do not overlap. When some of them overlap, the formula (15) will be Appropriate simplification, the displacement frequency response function that needs to be measured in the correction work will also be appropriately reduced;

For the case of acceleration frequency response, it is only necessary to multiply both ends of formula (15) by -ω ² to obtain the expression form of the acceleration frequency response function A,

表示悬挂状态下l、p点之间的加速度频响函数；

表示悬挂状态下n点加速度原点频响函数；A′₁₁，A′₂₂……A′_nn分别表示添加的虚拟支承在1、2……n点处的加速度频响函数。In the formula, A represents the acceleration frequency response function, and A _lp represents the acceleration frequency response function between points l and p of the free structure;

Indicates the acceleration frequency response function between points l and p in the suspended state;

Indicates the frequency response function of the acceleration origin of point n in the suspension state; A′ ₁₁ , A′ ₂₂ ... A' _nn represent the acceleration frequency response function of the added virtual support at points 1, 2...n, respectively.

中的支承影响。In order to verify the feasibility of the multi-point suspension support effect elimination method, the free beam modal test with two-point suspension is selected. As shown in Figure 6, the free beam is equally divided into five measuring points along the length direction, of which points 1 and 5 are suspension points, and each suspension point is equivalent to a support spring and a support damper. The dimensions and physical parameters of the beam are: 1×0.04×0.003m ³ and 7850kg/m ³ , respectively. The system parameters are selected as: k ₁ =600N/m, k ₅ =300N/m, c ₁ =0.3N·s/m, c ₅ =0.5N·s/m. Select the fourth point of the beam as the excitation point, and the second point as the response measurement point. The goal of this experiment is to eliminate the frequency response function

support effects in .

进行修正，修正后的频响函数为

According to formula (16) to

After correction, the frequency response function after correction is

为需要“测量的”频响函数，这里可直接对悬挂梁有限元建模计算获取。为了检验修正效果，需要将修正后的频响函数

和准确频响函数A₂₄进行对比，而A₂₄可通过自由梁有限元建模计算获取。如图7，相比于准确频响函数A₂₄，“测量的”频响函数

在悬挂支承的影响下，三阶共振峰均向右移动，并且在原第一阶共振峰左侧多出两个共振峰(约3.8Hz和7Hz处)。同时可看出，三阶共振峰的移动幅度，第一阶最大，第二节其次，第三阶最小。当消除悬挂支承影响后，修正后的频响函数

与准确的频响函数A₂₄完全一致，如图8所示。但如果仅消除支承影响中的支承刚度影响，而忽略支承阻尼，修正后的效果如图9所示，总体修正效果较好，但在共振峰处

幅值略小于A₂₄，反共振峰处

幅值略大于A₂₄，这种误差将导致提取的模态阻尼比不准确。因此，对于高质量模态测试，既要消除支承刚度的影响，还需考虑支承阻尼的影响。The right side of the above formula

For the "measured" frequency response function, it can be directly obtained by modeling and calculating the finite element of the suspension beam. In order to test the correction effect, the corrected frequency response function needs to be

It is compared with the accurate frequency response function A ₂₄ , and A ₂₄ can be obtained through free beam finite element modeling calculation. As shown in Figure 7, compared to the exact FRF A ₂₄ , the “measured” FRF

Under the influence of the suspension support, the third-order formant moves to the right, and there are two more formants (about 3.8Hz and 7Hz) on the left side of the original first-order formant. At the same time, it can be seen that the movement range of the third-order formant is the largest in the first order, followed by the second, and the smallest in the third. After eliminating the effect of the suspension support, the modified frequency response function

It is completely consistent with the accurate frequency response function A ₂₄ , as shown in FIG. 8 . However, if only the support stiffness effect in the support effect is eliminated, and the support damping is ignored, the corrected effect is shown in Figure 9. The overall correction effect is good, but at the resonance peak

The amplitude is slightly smaller than A ₂₄ , at the anti-resonant peak

The magnitude is slightly larger than A ₂₄ , and this error will lead to inaccurate extracted modal damping ratios. Therefore, for high-quality modal testing, it is necessary to eliminate the influence of support stiffness and also consider the influence of support damping.

Suspension support is a commonly used support method in modal test experiments, and it is mainly used to simulate free boundary conditions. However, the additional stiffness and damping introduced by this support method will have an impact on the measured frequency response function, especially when the stiffness of the measured structural member is small, the impact is very significant. Aiming at the free mode test of the suspension support mode, the invention proposes a method for eliminating the influence of the support from the measured frequency response function, and the support stiffness and support damping are considered in the support condition. The results show that: given the support stiffness k _s and support damping c _s , by measuring the frequency response function related to the suspension point, the influence of the suspension support stiffness and damping can be eliminated, and the frequency response function of the free structure can be obtained.

It should be understood that the parts not described in detail in this specification belong to the prior art.

It should be understood that the above-mentioned descriptions for the preferred embodiments are relatively detailed, and should not therefore be considered as limiting the scope of the patent protection of the present invention. Within the scope of protection, replacements or modifications can also be made, all of which fall within the protection scope of the present invention, and the scope of protection of the present invention should be based on the appended claims.

Claims (4)

1. A method for eliminating the influence of suspension support in the frequency response function for free mode testing, characterized in that: for single-point suspension, assuming that the self stiffness of structure C is small enough to ignore the influence of suspension support, structure C suspension At point s, the suspension support effect is equivalent to the spring with k _s stiffness and the damping with c _s , point p is the excitation point, and point l is the measurement point, where "p point" and "l point" are the Any two points; in order to eliminate the influence of the suspension support, a "virtual support" is applied at point s, and the "negative stiffness" k′ _s = -k _s and "negative damping" c′ _s = -c _s in the "virtual support" cancel The influence of the suspension support is eliminated, so that the structure is equivalent to a free state; For the convenience of analysis, point s is split into two points, s and s′, and in the “virtual support”, point s is expressed by point s′; Assuming that the suspended structure C is substructure I, and the "virtual support" is substructure II, the combination of substructure I and substructure II results in a free structure; Analyze substructures I and II separately; For substructure Ⅰ, the relationship between the output displacement response and the input force in the frequency domain is established,

Among them, X _l and X _s represent the displacement response of substructure I at points l and s, respectively, and F _p and R _s represent the forces on substructure I at points p and s, respectively;

Indicates the displacement frequency response function between points l and s in the suspended state;

Indicates the displacement frequency response function between points s and p in the suspended state;

Indicates the origin displacement frequency response function at point s in the suspended state;

Indicates the displacement frequency response function between points l and p in the suspended state; For substructure II, the relationship between the output displacement response and the input force is also established, X'_s' = α _s's' R _s' (2) In the formula,

Among them, X′ _s′ and R _s′ represent the displacement response and the acting force of substructure II at point s respectively; α _s′s′ represents the frequency response function of the origin displacement of substructure II at point s; jω where j is a complex unit, and ω is an independent variable of the frequency response function; The constraint conditions of force and displacement at connection point s or s′ are respectively R _s +R _s′ = 0 (4) X _s ＝X _s′ (5) Simultaneous formulas (1)～(5), get

In the formula, α _lp represents the displacement frequency response function between points l and p in free state;

Indicates the displacement frequency response function between points l and p in the suspension state; in order to avoid confusion, the frequency response function in the free state is named "accurate frequency response function", and the frequency response in the suspension state is "measured frequency response function", That is, α _lp is the exact frequency response function,

Both are measured frequency response functions; According to formula (6), it can be seen that the exact frequency response function α _lp and the measured frequency response function

There is a difference, and this difference is caused by the stiffness and damping of the support; and when the suspension stiffness k _s and damping c _s are given, the exact frequency can be calculated by measuring the frequency response function related to the suspension point s Response function α _lp , that is, to eliminate the frequency response function

The purpose of supporting influence. 2. the method for eliminating the influence of suspension support in the frequency response function for free mode testing according to claim 1 is characterized in that: for the situation of acceleration frequency response, formula (6) needs to be multiplied by -ω ² left and right, namely Get the relationship between acceleration frequency response and accurate acceleration frequency response (7)

In the formula, A represents the acceleration frequency response function, and A _lp represents the acceleration frequency response function between points l and p of the free structure;

Indicates the acceleration frequency response function between points l and p in the suspended state;

Indicates the acceleration frequency response function between points s and p in the suspended state;

Indicates the acceleration frequency response function between points l and s in the suspended state;

Represents the frequency response function of the acceleration origin at point s in the suspension state; as long as the support stiffness k _s and support damping c _s are known, the frequency response function _Alp of the free structure can be obtained by measuring the frequency response function related to the suspension point. 3. A method for eliminating the influence of suspension supports in the frequency response function for free mode testing, characterized in that: for multi-point suspension, it is assumed that the self-stiffness of structure C is small enough to ignore the influence of suspension supports, and structure C is in In the multi-point suspension state, the suspension points are 1, 2, ..., n respectively; the support stiffness of each suspension point is _ki , the damping size is ci, _i =1, 2, ..., n; point p is the excitation point, l point is the measurement point, where "point p" and "point l" are any two points on the structure; in order to eliminate the influence of suspension support, a "virtual support" is applied at each suspension point in turn, and the "virtual support" in "virtual support" Negative stiffness " _ki '=- _ki and "negative damping"c' _i = _-ci respectively counteract the influence of each suspension support, so as to obtain a structure in a free state; For the convenience of analysis, the suspension point s _i is split into two points s _i and s′ _i , and in the “virtual support”, s _i is used to express s _i ; The original suspended structure C is regarded as substructure I, and the virtual support is regarded as substructure II, III, ...; for substructure I, the relationship between the output displacement response and the input force in the frequency domain is established,

Among them, k=1, 2,..., n, X _l and X _k represent the displacement response of substructure I at point l and point k respectively, F _p ,

and R _i denote the acting force on substructure I at point p, S _i and i, respectively;

Indicates the displacement frequency response function between points l and p in the suspended state;

Indicates the displacement frequency response function between points l and S _i in the suspended state;

Indicates the displacement frequency response function between points k and p in the suspension state;

Indicates the displacement frequency response function between points k and i in the suspended state; For substructures II, III, ..., the relationship between the output displacement response and the input force is also established, X′ _k ＝α′ _kk R′ _k (10) In the formula,

Among them, X′ _k and R _k represent the displacement responses and _acting forces of substructures II, III, ... at point k, respectively; Origin displacement frequency response function; j in jω is a complex unit, and ω is an independent variable of frequency response function; The constraint conditions of force and displacement at connection point s or s′ are respectively: R _k + R′ _k = 0 (12) X _k = X′ _k (13) Simultaneous formula (8)～(13), get α ^(s) F=X (14) In the formula,

Solving formula (14), we get

In the formula, α _lp represents the displacement frequency response function between points l and p of the free structure;

...represents the displacement frequency response function of the suspended structure; α′ ₁₁ , α′ ₂₂ ...represents the origin displacement frequency response function of the added virtual support at points 1, 2... respectively; Equation (15) shows that for displacement frequency response function

The correction requires additional measurement of multiple displacement frequency response functions related to suspension points 1, 2...n, and the number of displacement frequency response functions required to be measured increases with the number of suspension points; It is deduced from formula (15), for the case of N-point suspension, the correction

Additional measurements (N ² +5N)/2 sets of displacement frequency response functions are required, which are the origin displacement frequency response functions

and across point displacement frequency response function

These displacement frequency response functions are all related to the suspension point; the above conclusion is for the case that the excitation point p, the response point l and the suspension point 1, 2...n do not overlap. When some of them overlap, the formula (15) will be With appropriate simplification, the frequency response function of displacement that needs to be measured in the correction work will also be appropriately reduced. 4. the method for eliminating the influence of suspension support in the frequency response function according to claim 3, is characterized in that: for the situation of acceleration frequency response, only need to multiply the two ends of formula (15) by -ω respectively ² That is, the expression form of the acceleration frequency response function A is obtained,

In the formula, A represents the acceleration frequency response function, and A _lp represents the acceleration frequency response function between points l and p of the free structure;

Indicates the acceleration frequency response function between points l and p in the suspended state;

Indicates the frequency response function of the acceleration origin at point n in the suspension state; A′ ₁₁ , A′ ₂₂ ... A′ _nn represent the acceleration frequency response functions of the added virtual support at points 1, 2...n respectively.

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