CN109635312B - Structure intermediate frequency vibration calculation method based on power flow method and statistical energy method - Google Patents
Structure intermediate frequency vibration calculation method based on power flow method and statistical energy method Download PDFInfo
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Abstract
The invention provides a structure intermediate frequency vibration calculation method based on a power flow method and a statistical energy method. And carrying out finite element coarse mesh division on the power flow model, forming a corresponding mass and rigidity matrix, establishing a structural power flow balance equation based on a power flow theory, and forming a structural energy influence coefficient matrix under a non-correlated excitation load. And establishing a structural coupling loss factor matrix according to the statistical energy model, and replacing the coupling loss factor by using the non-diagonal elements of the energy influence coefficient matrix to form a corrected statistical energy coupling loss factor matrix. And finally, establishing a new statistical energy balance equation of the structure according to the corrected coupling loss factor matrix, and calculating the medium-frequency vibration response of the structure by using a statistical energy method. The method does not need a fine grid, requires less resources for calculation, has high calculation speed, can overcome the assumption of weak coupling between the statistical energy method structures, and has low cost.
Description
Technical Field
The invention belongs to the technical field of engineering mechanics and vibration engineering, and particularly relates to a structural medium-frequency vibration calculation method based on a power flow method and a statistical energy method.
Background
The calculation of the sound vibration response of the structure middle frequency band has been a difficult problem in engineering, the structure has both a deterministic substructure and a statistical substructure in the middle frequency band, and the vibration of the structure shows the mixed vibration characteristic of coexistence of low mode and high mode. In a low frequency band, the finite element method can calculate the global mode of the structure, the low frequency sound vibration response of the structure is expressed through the amplitude and the phase, and good calculation accuracy is obtained. When the finite element method is used for structural vibration response calculation, 6-10 units in one wavelength need to be guaranteed in order to guarantee calculation accuracy, the number of required finite element units is increased along with the increase of analysis frequency, and calculation cost is inevitably increased. Meanwhile, the finite element method can only identify the low-order finite number of modes, the structural modes are more and more dense along with the increase of the frequency, and the finite element method cannot clearly identify the modes. The statistical energy method is generated according to the calculation of the sound vibration response of the high frequency band of the structure and is widely applied. Different from the finite element method, the statistical energy method predicts the energy transfer and energy response of each subsystem from the statistical angles of time, frequency domain and space average, and effectively solves the problem of calculating the sound vibration response of the structural high frequency band. However, the statistical energy method has many assumptions on application, such as weak coupling of coupling between substructures, sufficient resonance modes of the substructures, and a sufficiently high mode overlap coefficient, and the like, and the application of the statistical energy method in the calculation of the frequency acoustic vibration response in the structure is limited to a certain extent. In order to solve the defects of a finite element and a statistical energy method, an FE-SEA mixing method is provided by short P.J. and Langley R.S. and the like [1-3] based on a wave coupling theory, the structure is divided into a long wave (finite element) substructure and a short wave (statistical energy) substructure, the two substructures are coupled through mixing connection, and the calculation and analysis of the sound vibration response of the middle frequency band of the structural coupling system are realized. The FE-SEA hybrid method has a good effect in the prediction of the medium-frequency sound vibration of the structure, but has some existing problems which are worthy of continuous research, such as how to quantitatively distinguish a finite element substructure from a statistical energy substructure, how to solve the uncertainty of a coupling interface between subsystems, and the like.
No description or report of the similar technology to the invention is found at present, and similar data at home and abroad are not collected yet.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a structural medium-frequency vibration calculation method based on a power flow method and a statistical energy method.
The invention is realized by the following technical scheme.
A structure intermediate frequency vibration calculation method based on a power flow method and a statistical energy method comprises the following steps:
establishing a power flow model and a statistical energy model of a structure;
establishing a power flow balance equation of the structure for the power flow model by using a power flow method to form an energy influence coefficient matrix of the structure;
according to the statistical energy model, a statistical energy coupling loss factor matrix of the structure is established, and the coupling loss factor of the statistical energy coupling loss factor matrix is replaced by the non-diagonal elements of the energy influence coefficient matrix to form a corrected statistical energy coupling loss factor matrix;
and establishing a new statistical energy balance equation of the structure according to the corrected statistical energy coupling loss factor matrix, and calculating the medium-frequency vibration response of the structure by using the new statistical energy balance equation by using a statistical energy method.
Preferably, the method for establishing a power flow balance equation of the structure for the power flow model by using a power flow method to form an energy influence coefficient matrix of the structure comprises the following steps:
the method comprises the steps of carrying out finite element coarse mesh division on a power flow model, forming a corresponding mass matrix and a corresponding rigidity matrix, establishing a power flow balance equation of the structure based on a power flow method, and forming an energy influence coefficient matrix of the structure under a non-relevant excitation load.
Preferably, the power flow model is subjected to finite element coarse meshing, and a corresponding mass matrix and a corresponding stiffness matrix are formed, and the method comprises the following steps:
discretizing the power flow model into finite element units;
assuming a shape function representing the physical behavior of the unit, and establishing an equation for the unit;
and combining the units to construct a corresponding mass matrix and a corresponding rigidity matrix.
Preferably, discretizing the power flow model into finite element elements means decomposing the power flow model into nodes and elements.
Preferably, assuming a shape function representing the physical behavior of a cell means that an approximately continuous function representing the cell solution is assumed.
Compared with the prior art, the invention has the following beneficial effects:
compared with a finite element method, the structure intermediate frequency vibration calculation method based on the power flow method and the statistical energy method does not need a fine grid, requires less resources for calculation and has high calculation speed; meanwhile, the coupling loss factor calculated by using the power flow method is more accurate than that of a statistical energy method, and the assumption of weak coupling between sub-structures of the statistical energy method can be overcome. The calculation method combining the power flow method and the statistical energy method, provided by the invention, can obtain higher calculation precision of the medium-frequency vibration response of the structure than that of the statistical energy method for a large-scale complex structure, and save a large amount of calculation cost than that of a finite element method.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
fig. 1 is a schematic structural diagram of a vibration analysis required in an embodiment of the present invention.
Fig. 2 (a) is a graph showing the comparison of the frequency vibration velocity of the plate 1 structure calculated by different methods in the embodiment of the present invention.
Fig. 2 (b) is a graph comparing the medium frequency vibration velocity of the plate 2 structure calculated by different methods in the embodiment of the present invention.
Fig. 3 is a flow chart of a structure intermediate frequency vibration calculation method based on a power flow method and a statistical energy method provided by the invention.
Detailed Description
The following examples illustrate the invention in detail: the embodiment is implemented on the premise of the technical scheme of the invention, and gives a detailed implementation mode and a specific operation process. It should be noted that various changes and modifications can be made by those skilled in the art without departing from the spirit of the invention, and these changes and modifications are all within the scope of the invention.
Examples
The embodiment provides a structure intermediate frequency vibration calculation method based on a power flow method and a statistical energy method, which comprises the following steps:
establishing a power flow model and a statistical energy model of a structure needing vibration analysis;
discretizing the power flow model into finite element units, i.e. decomposing the structure into nodes and units;
assuming a shape function representing the physical behavior of the unit, namely assuming an approximate continuous function representing the solution of the unit, and establishing an equation for the unit;
combining the units to construct an overall stiffness matrix and a mass matrix of the structure;
establishing a power flow balance equation of the structure by using a power flow method, calculating the vibration energy of the power flow model under non-correlated excitation, and constructing an energy influence coefficient matrix of the structure;
according to the statistical energy model, a statistical energy coupling loss factor matrix of the structure is established, and the coupling loss factors of the statistical energy coupling loss factor matrix are replaced by the non-diagonal elements of the energy influence coefficient matrix;
updating the statistical energy coupling loss factor matrix, establishing a new statistical energy balance equation of the structure, and solving the medium-frequency vibration response of the structure through the new statistical energy balance equation based on a statistical energy method.
In this embodiment:
the structure intermediate frequency vibration calculation method based on the power flow method and the statistical energy method is a combination of the statistical energy method and the power flow method for realizing the structure intermediate frequency vibration calculation.
The method comprises the steps of preprocessing a structure needing vibration analysis, establishing a power flow model, carrying out discretization processing on the power flow model according to structural shape characteristics, and establishing a mass matrix and a rigidity matrix.
And after discretizing the structure, obtaining an energy influence coefficient matrix of the structure by using a power flow method.
And establishing a statistical energy model, and constructing a statistical energy coupling loss factor matrix of the structure.
And replacing the coupling loss factors in the energy coupling loss factor matrix according to the obtained energy influence coefficient matrix off-diagonal elements.
And establishing a new statistical energy balance equation of the structure according to the corrected statistical energy coupling loss factor matrix, and calculating the medium-frequency vibration response of the structure by using a statistical energy method.
The technical solutions provided by the above embodiments of the present invention are further described in detail below with reference to a specific application example.
The structure intermediate frequency vibration calculation method based on the power flow method and the statistical energy method provided by the embodiment of the invention is suitable for various different structures, only one example of applying the method to a three-plate coupling structure is provided here, and the method is similar for other different structures and is not repeated.
The specific application example is described in more detail below by way of example with reference to the accompanying drawings:
discretizing the three-plate coupling structure in fig. 1, applying broadband non-correlated excitation in the middle of the plate 1, and obtaining a power flow balance equation of the structure by using a power theory (a power flow method) as follows:
E(ω)＝[EIC(ω)]P in (ω) (1)
in the formula, E (omega) is an energy matrix of each subsystem in the power flow model; p is in (ω) an input power matrix for the external excitation subsystem; ω is the center frequency of the analyzed band; [ EIC (ω)]Is an energy influencing coefficient matrix.
In the formula, c mn And when the nth substructure is input with unit power, representing the energy of the mth substructure.
The statistical energy balance equation for the structure is:
ωηE(ω)＝P in (ω) (3)
where ω is the center frequency of the analyzed band; eta i Is the internal loss factor of subsystem i; eta ij Indicating energy transfer from subsystem iA one-way coupling loss factor to subsystem j; e (omega) is an energy matrix of each subsystem in the statistical energy model; p in And (omega) is an input power matrix of the external excitation subsystem.
From formula (3), one can obtain:
comparing equation (1) and equation (5), the off-diagonal elements of the [ EIC (ω) ] inverse matrix can be equivalent to coupling loss factors describing the energy transfer between substructures, which is the junction of the two methods in the above embodiments of the present invention.
And after obtaining the equivalent coupling loss factor among the substructures, updating the coupling loss factor matrix of the three-plate coupling structure, applying 1N excitation force at the center of the plate 1, calculating the vibration response of the three-plate coupling structure by using a statistical energy method, and calculating the frequency range to be 400-800Hz. To verify the superiority and accuracy of the method provided by the above embodiment of the present invention, the vibration response of the structure was calculated by using the finite element method, the finite element-statistical energy mixing method, and the statistical energy method, respectively, for the same structure, as shown in fig. 2 (a) and 2 (b). In order to ensure the computation accuracy of the finite element method, the requirement of at least 6 units in one wavelength is ensured when discretization processing is performed on the structure, the number of the finally obtained units is 20000, and table 1 shows the time consumption and accuracy comparison of the structure intermediate-frequency vibration computation of different methods in the specific application example.
TABLE 1 comparison of different methods for calculating intermediate frequency vibration
As can be seen from fig. 2 (a) and 2 (b), in the intermediate frequency region (400-800 Hz), compared with the finite element-statistical energy mixing method and the statistical energy method, although the vibration speed of the plate 1 and the plate 2 obtained by the method provided by the above embodiment of the present invention has a certain error in amplitude, the calculated results of the finite element method have better consistency in overall trend, which indicates that the method provided by the above embodiment of the present invention can improve the calculation accuracy of the statistical energy method in the prediction of the structural intermediate frequency vibration response, and effectively expand the application frequency range of the statistical energy method.
As can be seen from Table 1, the method provided by the above embodiment of the present invention is superior to the finite element method in terms of calculation speed, and superior to the statistical energy method and the finite element-statistical energy hybrid method in terms of calculation precision, and the method provided by the above embodiment of the present invention has better applicability and reliability in the calculation of the frequency vibration in the structure.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.
Claims (2)
1. A structure intermediate frequency vibration calculation method based on a power flow method and a statistical energy method is characterized by comprising the following steps:
establishing a power flow model and a statistical energy model of a structure;
establishing a power flow balance equation of the structure for the power flow model by using a power flow method to form an energy influence coefficient matrix of the structure;
the method for establishing the power flow balance equation of the structure on the power flow model by using the power flow method to form the energy influence coefficient matrix of the structure comprises the following steps:
carrying out finite element coarse mesh division on a power flow model, forming a corresponding mass matrix and a corresponding rigidity matrix, establishing a power flow balance equation of the structure based on a power flow method, and forming an energy influence coefficient matrix of the structure under a non-correlated excitation load; the power flow balance equation is as follows:
E(ω)＝[EIC(ω)]P in (ω)
in the formula, E (omega) is an energy matrix of each subsystem in the power flow model; p in (ω) is the input power matrix of the external excitation subsystem; ω is the center frequency of the analyzed band; [ EIC (ω)]Is an energy influence coefficient matrix;
in the formula, c mn Representing the energy of the mth substructure when the nth substructure inputs unit power;
the method for carrying out finite element coarse mesh division on the power flow model and forming a corresponding mass matrix and a corresponding rigidity matrix comprises the following steps:
discretizing the power flow model into finite element units;
assuming a shape function representing the physical behavior of the unit, and establishing an equation for the unit;
combining the units to construct a corresponding mass matrix and a corresponding rigidity matrix;
assuming a shape function representing the physical behavior of a cell means that an approximately continuous function representing the solution of the cell is assumed;
according to the statistical energy model, a statistical energy coupling loss factor matrix of the structure is established, and the coupling loss factor of the statistical energy coupling loss factor matrix is replaced by the non-diagonal elements of the energy influence coefficient matrix to form a corrected statistical energy coupling loss factor matrix;
and establishing a new statistical energy balance equation of the structure according to the corrected statistical energy coupling loss factor matrix, and calculating the medium-frequency vibration response of the structure by using the new statistical energy balance equation by using a statistical energy method.
2. The structure medium-frequency vibration calculation method based on the power flow method and the statistical energy method as claimed in claim 1, wherein discretizing the power flow model into finite element units means decomposing the power flow model into nodes and units.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006071570A (en) * | 2004-09-06 | 2006-03-16 | Canon Inc | Method of analyzing vibration |
| CN102411673A (en) * | 2011-08-18 | 2012-04-11 | 西北工业大学 | Method for calculating intermediate and high frequency dynamic response of acoustic vibration system |
| CN106844906A (en) * | 2017-01-04 | 2017-06-13 | 东南大学 | Statistic energy analysis parameter acquiring method based on FInite Element and power input method |
| CN107368630A (en) * | 2017-06-23 | 2017-11-21 | 东南大学 | A kind of numerical method for obtaining coupling loss factor |
| CN108491595A (en) * | 2018-03-07 | 2018-09-04 | 东南大学 | Gu a kind of high frequency partial of sound-coupled structure responds predicting method |
-
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006071570A (en) * | 2004-09-06 | 2006-03-16 | Canon Inc | Method of analyzing vibration |
| CN102411673A (en) * | 2011-08-18 | 2012-04-11 | 西北工业大学 | Method for calculating intermediate and high frequency dynamic response of acoustic vibration system |
| CN106844906A (en) * | 2017-01-04 | 2017-06-13 | 东南大学 | Statistic energy analysis parameter acquiring method based on FInite Element and power input method |
| CN107368630A (en) * | 2017-06-23 | 2017-11-21 | 东南大学 | A kind of numerical method for obtaining coupling loss factor |
| CN108491595A (en) * | 2018-03-07 | 2018-09-04 | 东南大学 | Gu a kind of high frequency partial of sound-coupled structure responds predicting method |
Non-Patent Citations (1)
| Title |
|---|
| 基于有限元能量流模型的复杂耦合结构中低频段耦合损耗因子的计算;卢兆刚等;《振动与冲击》;20111125(第11期);全文 * |
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