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Structural vibration analysis method based on finite element method and generalized Fourier series method

A technology of Fourier series and finite element method, which is applied in the field of structural vibration analysis based on finite element method and generalized Fourier series method, to achieve the effects of saving calculation costs, less resources required for calculation, and high precision

Inactive Publication Date: 2010-11-17
HARBIN ENG UNIV
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Problems solved by technology

[0005] The purpose of the present invention is to provide a structural vibration analysis method based on the finite element method and the generalized Fourier series method that can be used to solve the calculation problems of large and complex structural vibrations, especially medium and high frequency vibrations

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  • Structural vibration analysis method based on finite element method and generalized Fourier series method
  • Structural vibration analysis method based on finite element method and generalized Fourier series method
  • Structural vibration analysis method based on finite element method and generalized Fourier series method

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Embodiment approach 1

[0031] combine figure 2 , the left part of the cantilever beam support is expressed by the finite element fa, and the right part of the support is expressed by the Fourier series expansion method. The basic equation of the beam bending problem can be expressed as follows:

[0032] geometric relationship κ = - d 2 w dx 2 - - - ( 1 )

[0033] Stress-strain relationship M = EIκ = - EI d 2 w d x 2 - - - ( 2 )

[0034] balance equation Q = dM dx ...

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Abstract

The invention aims at providing a structural vibration analysis method based on a finite element method and a generalized Fourier series method, which comprises the following steps of: dividing a structure region to be subjected to vibration analysis to respectively and correspondingly form a finite element expression region and a generalized Fourier series expression region; dividing the finite element grids of the finite element expression region to form a corresponding quality stiffness matrix, and selecting a corresponding assumption displacement form according to the characteristics of the generalized Fourier series expression region to form a quality stiffness matrix; subsequently, establishing a virtual spring between the two regions, and converting the potential energy of the virtual spring into an overall coupling stiffness matrix by using an energy variation method; then, arranging the formed quality stiffness matrices according to displacement to form an overall structure quality stiffness matrix; and solving linear equations to obtain an unknown coefficient in corresponding node displacement and series expansion. When applied to a large complex structure, the method not only can obtain precision higher than the finite element method, but also can save a large amount of calculation cost.

Description

technical field [0001] The invention relates to a structural vibration analysis method applied in the fields of engineering mechanics and vibration engineering. Background technique [0002] As a numerical calculation method, the finite element method has been widely used in the field of structural vibration. In dealing with irregular and complex structures, this method has incomparable advantages over analytical methods. However, the finite element method still has some shortcomings. For example, in the calculation of large and complex structures, especially high-frequency problems or even intermediate-frequency problems, due to the limitations of current computing technology, too many meshes are required for calculation, making it very difficult or even impossible to solve. [0003] In the structural vibration analysis, the analytical method has the advantages of accurate results, and the use of computers to solve the results has the advantages of wide frequency band of c...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
Inventor 李玩幽吕秉琳周海军率志君郭宜斌
Owner HARBIN ENG UNIV
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