CN111274704A - Method for re-analyzing dynamic characteristics of structure after addition of substructure - Google Patents
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Abstract
The invention discloses a structure dynamics characteristic re-analysis method after adding a substructure, which comprises the steps of firstly determining a structure local modification position and modified contents (the structure local modification refers to adding subsystems at some local positions of an original structure), then obtaining an original structure frequency response function (excitation points and response measurement points related to the frequency response function cover the structure local modification position points), and finally calculating the frequency response function of the modified structure according to a calculation formula provided by the method; the method can calculate the frequency response function of the locally modified structure at multiple points at one time based on the frequency response function of the original structure, so that the dynamic characteristics of the modified structure are re-analyzed, the design efficiency is improved, the design blindness is avoided, the design cost is reduced, and the method has practical engineering application value.
Description
Technical Field
The invention belongs to the technical field of structural dynamics, relates to a method for analyzing the dynamic characteristics of a structure added with a spring mass quantum structure, and particularly relates to a method for re-analyzing the dynamic characteristics of a structure added with a spring mass quantum structure based on an original structure frequency response function model. Here, adding a spring mass substructure refers to adding a spring mass substructure to one or more coordinates of the original structure.
Background
In engineering, modifications to the designed structure are required in order to improve certain characteristics of the structure. In essence, structural modifications are to change the mass, stiffness or damping parameter values of existing structures to allow the system to meet certain specific dynamic property requirements. For some complex structures in engineering, the adjustment of the system mass, stiffness or damping parameter values is difficult to realize physically. Moreover, some designed structures meeting specific functional requirements do not allow the internal structural form to be changed, and thus the mass matrix, the stiffness matrix or the damping matrix of the existing structure cannot be adjusted. A better solution to this problem is to modify the structure by adding a spring-mass substructure outside the original structure. Since the structural modification scheme is usually not unique, it is necessary to re-analyze the dynamics of different schemes before implementing the modification scheme, and to find the optimal scheme according to the theoretical analysis result, so as to avoid the blindness of modification and reduce the design cost. Re-analysis of the dynamic characteristics of the modified structure requires a relevant dynamic model based on the original structure, such as a modal model (composed of modal frequency and modal vector), a spatial state model (composed of mass matrix, stiffness matrix and damping matrix), a frequency response function model (composed of frequency response function) and the like. The frequency response function can be directly obtained through test measurement, and is easy to obtain and accurate. Therefore, the method for analyzing the dynamic characteristics of the added substructure of the structure based on the frequency response function has important engineering significance.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method for re-analyzing the dynamic characteristics of a structure added with a spring mass quantum structure based on an original structure frequency response function model, belongs to the research category of 'positive problems' in structural dynamic modification, and aims to improve the design efficiency, avoid the design blindness and reduce the design cost.
The technical scheme adopted by the invention is as follows: a method for analyzing the dynamic characteristics of a structure after adding a substructure is characterized by comprising the following steps: assuming that the vibration differential equation of a general linear n-degree-of-freedom undamped system is expressed as:
in the formula, f is an acting force vector; k and M are respectively a rigidity matrix and a mass matrix of an original structure, and x represents a displacement vector;
representing an acceleration vector.
Let the vibration system respond by x ueiωtAnd substituting it into the formula (1) to obtain
In the formula, Zn×nThe dynamic stiffness matrix is of an original structure; ω represents a frequency variable; f represents an action force vector; i represents an imaginary unit; t represents a unit of time; u represents the vibration amplitude and f represents the force vector; u. ofiRepresenting the vibration amplitude at the ith position.
Assuming that the acceleration frequency response function matrix of the original structure is A, the positions to be modified are respectively positioned at 1 and 2 … … j (j is less than or equal to n) points on the structure, and the modification mode is that the spring stiffness delta k is respectively added at each point1，Δk2……ΔkjMass is Δ m1，Δm2……ΔmjThe spring mass substructure of (a);
the method comprises the following steps:
step 1: dynamic stiffness of the original structure is Zn×nThe dynamic stiffness of the structure after the spring mass substructure is increased can be equivalent to Zn×n+ Δ Z, Δ Z is expressed in the form of a diagonal matrix as follows.
Where ω represents the frequency variable, Δ m represents the added mass, Δ k represents the added spring rate, and the substructure amplitude is Δ u;
the delta Z is:
in the formula of UkRepresents a j × 1 column vector with the k-th row element being 1 and the other elements being zero, VkIndicates the k-th row element is
A j x 1 column vector with other elements of zero, i.e.
Step 2: converting the acceleration frequency response function matrix A of the original structure into a displacement frequency response function matrix H;
A＝-ω2H (4)；
and step 3: calculating frequency response function matrix H of structure after adding spring mass quantum structure*；
H*＝H-H[U1… Uj]W-1[V1 T… Vj T]TH (5)
Wherein the content of the first and second substances,
the specific implementation of the step 3 comprises the following substeps:
step 3.1: the dynamic stiffness matrix of the original structure is assumed as follows:
Z＝K-Mω2(6)
in the formula, Z is a dynamic stiffness matrix of an original structure; k and M are respectively a rigidity matrix and a mass matrix of the original structure;
adding a spring mass quantum structure to the ith coordinate position of the original structure system, wherein the motion equation of the added structure is as follows:
Z-1u＝(ω2ΔM-ΔK)u+f (7)
after a substructure is added, an additional degree of freedom is added to the original structure, and the structure after the substructure is added is represented in a matrix form:
wherein u isiShowing the vibration amplitude of the i-th position, fiIndicating the force at the ith position.
The last line of the equation relationship of equation (8)
Substituting the formula (9) into the formula (8),
from row i and last row of the matrix of equation (10):
that is, equation (8) is written as:
namely, in the n-degree-of-freedom structure, after a spring mass quantum structure is added in the ith degree of freedom, the dynamic stiffness of the structure is changed as follows:
in the formula, Z*The dynamic stiffness matrix is a structure with a spring mass quantum structure; from the formula (6) to the formula (13), when a spring mass substructure is added to the ith degree of freedom of the n-degree-of-freedom structure, the method is equivalent to making the dynamic stiffness of the ith degree of freedom
A change in (c);
when the modification involves j degrees of freedom, the structural dynamic stiffness matrix becomes now:
Δ Z is expressed as:
then inverting equation (14) yields:
Z*-1＝(Z+ΔZ)-1＝Z-1-Z-1[U1… Uj]W-1[V1 T… Vj T]TZ-1(15)
in the formula (I), the compound is shown in the specification,
because the dynamic stiffness matrix and the frequency response function matrix of the structure are inverse matrixes, the method comprises the following steps:
Z*-1＝H*＝H-H[U1… Uj]W-1[V1 T… Vj T]TH (17)
in the formula, H is a frequency response function matrix of an original structure; h*Is a matrix of frequency response functions of the structure after adding additional mass, additional stiffness and additional damping.
And 4, step 4: using formula (4) to modify the displacement frequency response function matrix H of the structure*Conversion into acceleration frequency response function matrix A*。
The method provided by the invention can calculate the frequency response function of the structure after local modification at multiple points (the local modification of the structure refers to adding the spring mass subsystem at some local positions of the original structure) at one time based on the frequency response function of the original structure, so that the dynamic characteristics of the modified structure are re-analyzed, the design efficiency is improved, the design blindness is avoided, the design cost is reduced, and the method has practical engineering application value.
Drawings
FIG. 1 is a schematic diagram of a cantilever modal test model according to an embodiment of the present invention;
FIG. 2 shows a frequency response function A according to an embodiment of the present invention22Comparing the original value with the modified value to obtain a schematic diagram;
FIG. 3 shows a frequency response function A according to an embodiment of the present invention24Comparing the original value with the modified value to obtain a schematic diagram;
FIG. 4 shows a frequency response function A according to an embodiment of the present invention26The accurate value of (1), original value and modified value are compared with the diagram.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
The invention provides a method for re-analyzing a structure based on an original structure frequency response function model and adding a spring mass quantum structure to obtain dynamic characteristics, which comprises the following steps of:
step 1: the differential equation of vibration assuming a generally linear n-degree-of-freedom undamped system is expressed as
In the formula, f is an acting force vector; k and M are respectively a rigidity matrix and a mass matrix of the original structure;
let the vibration system respond by x ueiωtAnd substituting it into the formula (1) to obtain
Zn×nThe dynamic stiffness matrix is of an original structure;
step 2: suppose that a spring mass quantum structure is added to the ith degree of freedom, the mass of the substructure is Δ m, the spring stiffness is Δ k, and the amplitude is Δ u. Due to the addition of a spring mass quantum structure, an additional degree of freedom is also added to the original structure. Therefore, the motion equation of the modified system can be obtained by amplifying (2)
N +1 of the formula (3) is
Δkui+(-Δk+ω2Δm)Δu＝0
Namely, it is
Substituting the formula (4) into the formula (3) can obtain
The ith and n +1 th lines of equation (5) may be expressed as
Thus equation (3) can be written as
In the formula Z*The dynamic stiffness matrix is added with the spring mass quantum structure; Δ Z represents a modified stiffness matrix;
therefore, the structure of adding the spring mass quantum structure to the ith degree of freedom of the system can be expressed as that the dynamic stiffness value of the ith degree of freedom of the original structure is
Modification of (2).
Assuming now that the local modification of the structure (where the modification is the addition of a spring-mass substructure at a location point) involves j location points, Δ Z can be expressed by equation (8)
UkRepresents a j × 1 column vector with the k-th row element being 1 and the other elements being zero, VkIndicates the k-th row element is
A j × 1 column vector with other elements of zero; namely, it is
Then inverting equation (7) yields:
Z*-1＝(Z+ΔZ)-1＝Z-1-Z-1[U1… Uj]W-1[V1 T… Vj T]TZ-1(9)
in the formula (I), the compound is shown in the specification,
because the dynamic stiffness matrix and the frequency response function matrix of the structure are inverse matrixes to each other, the method has the advantages that
Z*-1＝H*＝H-H[U1… Uj]W-1[V1 T… Vj T]TH (11)
In the formula, H is a frequency response function matrix of an original structure; h*A frequency response function matrix of the structure after the addition of the substructure;
from the formula (11), when the frequency response function matrix H of the original structure and the added spring mass quantum structure are known, the frequency response function matrix H of the modified structure can be calculated*。
It should be noted that, the frequency response function matrices H and H mentioned above are both displacement frequency response function matrices. In engineering practice, the acceleration sensor is mostly adopted to measure response, the acceleration frequency response function A is directly obtained, the acceleration frequency response function A and the acceleration frequency response function A have the relation of a formula (12),
A＝-ω2H (12)
therefore, if the acceleration frequency response function matrix A of the original structure is given in practical application, the displacement frequency response function matrix H can be obtained by calculation according to the formula (12), and then the displacement frequency response function matrix H of the modified structure is calculated by substituting the formula (10) and the formula (11),
H*the expression of (a) is as follows:
H*＝H-H[U1… Uj]W-1[V1 T… Vj T]TH (13)
and finally, substituting the formula (12) to calculate an acceleration frequency response function A of the modified structure.
The invention is described in further detail below with reference to the figures and examples.
FIG. 1 is a cantilever modal test model with physical parameters shown in Table 1. The cantilever beam is dispersed along the length direction to be 6 equal parts, 6 measuring points are evenly distributed. Assuming that a spring-mass substructure is added at points 2, 4 and 6, respectively, the spring rate Δ k2、Δk4And Δ k6The sizes are 3000N/m, 4000N/m and 5000N/m respectively; suppose that masses are added at points 2, 4 and 6, respectively, with an additional mass Δ m2、Δm4And Δ m6The sizes are respectively 0.35Kg, 0.42Kg and 0.39 Kg. The excitation mode adopts a hammering method to excite the positions of 2, 4 and 6 points respectively. The aim of the embodiment is to analyze the frequency response function of the structure after the spring mass quantum structure is added according to the frequency response function of the original structure (namely the cantilever beam).
TABLE 1 cantilever beam physics parameter table
According to the method, in order to calculate the frequency response function of the modified structure, the frequency response function matrix of the original structure needs to be given. In this embodiment, the original structural acceleration frequency response function matrix a is obtained by numerical calculation and is recorded as an "original value".
And then converting the acceleration frequency response function of the original structure into a displacement frequency response function according to a formula (12), substituting the displacement frequency response function into formulas (10) and (11), and calculating a displacement frequency response function matrix H of the modified structure. And finally, calculating according to a formula (12) to obtain a corrected acceleration frequency response function matrix A, and recording as a 'modified value'. For comparison convenience, the acceleration frequency response function matrix of the cantilever beam structure added with the additional spring, the additional damping and the additional mass is also obtained in a numerical calculation mode and is recorded as an accurate value A';
for simplicity, only frequency response function A will be discussed herein22、A24And A26See fig. 2, fig. 3 and fig. 4 for the modification results. It can be seen that the frequency of each order of the frequency response function changes to some extent due to the influence of the added spring mass substructure. Generally, when a spring mass substructure is added to the original structure, the degree of freedom of the modified structure is increased by one, and thus a formant is also added to the frequency response function diagram. As shown in fig. 2, 3 and 4, a spring mass substructure is added to the original structure coordinates 2, 4 and 6, and three additional formants are added in the frequency range of 0-70 Hz, which is also because the system has three degrees of freedom. In addition, the formant frequencies of the modified system all change due to the addition of the spring mass substructure. The frequency response function of the modified structure calculated by the method provided by the invention
And
respectively obtaining accurate frequency response functions A 'through calculation with preset numerical values'22、A′24And A'26The method is completely matched, thereby verifying the effectiveness of the method.
It should be understood that parts of the specification not set forth in detail are prior art; the above description of the preferred embodiments is intended to be illustrative, and not to be construed as limiting the scope of the invention, which is defined by the appended claims, and all changes and modifications that fall within the metes and bounds of the claims, or equivalences of such metes and bounds are therefore intended to be embraced by the appended claims.
Claims (2)
1. A method for re-analyzing the dynamic characteristics of a structure after adding a substructure is characterized by comprising the following steps: assuming that the vibration differential equation of a general linear n-degree-of-freedom undamped system is expressed as:
in the formula, f is an acting force vector; k and M are respectively a rigidity matrix and a mass matrix of the original structure; x represents a displacement vector;
represents an acceleration vector;
let the vibration system respond by x ueiωtAnd substituting it into the formula (1) to obtain
In the formula, Zn×nThe dynamic stiffness matrix is of an original structure; ω represents a frequency variable; i represents an imaginary unit; t represents a unit of time; u represents the vibration amplitude and f represents the force vector; u. ofiRepresenting the vibration amplitude at the ith position;
assuming that the acceleration frequency response function matrix of the original structure is A, the positions to be modified are respectively positioned at 1 and 2 … … j points on the structure, and the modification mode is that the spring stiffness delta k is respectively added at each point1，Δk2……ΔkjMass is Δ m1，Δm2……ΔmjThe spring mass substructure of (a); wherein j is less than or equal to n;
the method comprises the following steps:
step 1: dynamic stiffness of the original structure is Zn×nThe dynamic stiffness of the structure after the spring mass substructure is increased is equivalent to Zn×n+ Δ Z, Δ Z is expressed in the form of a diagonal matrix;
where ω represents the frequency variable, Δ m represents the added mass, Δ k represents the added spring rate, and the substructure amplitude is Δ u;
the delta Z is:
in the formula of UkRepresents a j × 1 column vector with the k-th row element being 1 and the other elements being zero, VkIndicates the k-th row element is
A j x 1 column vector with other elements of zero, i.e.
Step 2: converting the acceleration frequency response function matrix A of the original structure into a displacement frequency response function matrix H;
A＝-ω2H (4)；
and step 3: calculating frequency response function matrix H of structure after adding spring mass quantum structure*；
H*＝H-H[U1…Uj]W-1[V1 T…Vj T]TH (5)
Wherein the content of the first and second substances,
and 4, step 4: using formula (4) to modify the displacement frequency response function matrix H of the structure*Conversion into acceleration frequency response function matrix A*。
2. The method for re-analyzing the dynamic characteristics of the structure after the addition of the substructure as claimed in claim 1, wherein the step 3 comprises the following sub-steps:
step 3.1: the dynamic stiffness matrix of the original structure is assumed as follows:
Z＝K-Mω2(6)
in the formula, Z is a dynamic stiffness matrix of an original structure; k and M are respectively a rigidity matrix and a mass matrix of the original structure;
adding a spring mass quantum structure to the ith coordinate position of the original structure system, wherein the motion equation of the added structure is as follows:
Z-1u＝(ω2ΔM-ΔK)u+f (7)
after a substructure is added, an additional degree of freedom is added to the original structure, and the structure after the substructure is added is represented in a matrix form:
wherein u isiShowing the vibration amplitude of the i-th position, fiIndicating the force at the ith position;
the last line of the equation relationship of equation (8)
Substituting the formula (9) into the formula (8),
from row i and last row of the matrix of equation (10):
that is, equation (8) is written as:
namely, in the n-degree-of-freedom structure, after a spring mass quantum structure is added in the ith degree of freedom, the dynamic stiffness of the structure is changed as follows:
in the formula, Z*The dynamic stiffness matrix is a structure with a spring mass quantum structure; from the formula (6) to the formula (13), when a spring mass substructure is added to the ith degree of freedom of the n-degree-of-freedom structure, the method is equivalent to making the dynamic stiffness of the ith degree of freedom
A change in (c);
when the modification involves j degrees of freedom, the structural dynamic stiffness matrix becomes now:
Δ Z is expressed as:
then inverting equation (14) yields:
Z*-1＝(Z+ΔZ)-1＝Z-1-Z-1[U1…Uj]W-1[V1 T…Vj T]TZ-1(15)
in the formula (I), the compound is shown in the specification,
because the dynamic stiffness matrix and the frequency response function matrix of the structure are inverse matrixes, the method comprises the following steps:
Z*-1＝H*＝H-H[U1…Uj]W-1[V1 T…Vj T]TH (17)
in which H is the original structureA frequency response function matrix; h*Is a matrix of frequency response functions of the structure after adding additional mass, additional stiffness and additional damping.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112329331A (en) * | 2020-10-15 | 2021-02-05 | 湖北工业大学 | Natural frequency and vibration mode configuration method based on mixed addition of mass and rigidity |
| CN112329332A (en) * | 2020-10-15 | 2021-02-05 | 湖北工业大学 | Intrinsic frequency and vibration mode configuration method based on added rigidity |
| CN112329333A (en) * | 2020-10-15 | 2021-02-05 | 湖北工业大学 | Method for configuring natural frequency and vibration mode based on added mass |
| CN112345642A (en) * | 2020-10-28 | 2021-02-09 | 扬州大学 | Harvester health monitoring method considering primary and secondary structure decomposition equivalence |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2002073334A2 (en) * | 2000-10-20 | 2002-09-19 | Sbi-Moldyn, Inc. | Method of providing integration of atomistic and substructural multi-body dynamics |
| GB0507618D0 (en) * | 2005-04-15 | 2005-05-25 | Lms Internat Nv | Method and system for dynamic analysis of complex systems |
| CN109241559A (en) * | 2018-08-01 | 2019-01-18 | 东南大学 | A kind of composite material elastic parameter recognition methods based on minor structure |
| CN110569587A (en) * | 2019-08-29 | 2019-12-13 | 湖北工业大学 | method for estimating dynamic characteristics of locally modified structure based on frequency response function |
-
2020
- 2020-01-20 CN CN202010067271.4A patent/CN111274704B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2002073334A2 (en) * | 2000-10-20 | 2002-09-19 | Sbi-Moldyn, Inc. | Method of providing integration of atomistic and substructural multi-body dynamics |
| GB0507618D0 (en) * | 2005-04-15 | 2005-05-25 | Lms Internat Nv | Method and system for dynamic analysis of complex systems |
| CN109241559A (en) * | 2018-08-01 | 2019-01-18 | 东南大学 | A kind of composite material elastic parameter recognition methods based on minor structure |
| CN110569587A (en) * | 2019-08-29 | 2019-12-13 | 湖北工业大学 | method for estimating dynamic characteristics of locally modified structure based on frequency response function |
Non-Patent Citations (1)
| Title |
|---|
| 杨智春: "结构动力学有限元模型修正的目标函数及算法", 《应用力学学报》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112329331A (en) * | 2020-10-15 | 2021-02-05 | 湖北工业大学 | Natural frequency and vibration mode configuration method based on mixed addition of mass and rigidity |
| CN112329332A (en) * | 2020-10-15 | 2021-02-05 | 湖北工业大学 | Intrinsic frequency and vibration mode configuration method based on added rigidity |
| CN112329333A (en) * | 2020-10-15 | 2021-02-05 | 湖北工业大学 | Method for configuring natural frequency and vibration mode based on added mass |
| CN112329332B (en) * | 2020-10-15 | 2022-04-15 | 湖北工业大学 | Intrinsic frequency and vibration mode configuration method based on added rigidity |
| CN112345642A (en) * | 2020-10-28 | 2021-02-09 | 扬州大学 | Harvester health monitoring method considering primary and secondary structure decomposition equivalence |
| CN112345642B (en) * | 2020-10-28 | 2023-03-24 | 扬州大学 | Harvester health monitoring method considering primary and secondary structure decomposition equivalence |
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