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Method for analyzing vibration in structural surface of rectangular plate under non-uniform elastic constrained boundary condition

A technology of elastic constraints and boundary conditions, applied in the direction of complex mathematical operations, etc., can solve problems such as inability to solve boundary constraints, springs satisfying non-uniform distribution, etc.

Active Publication Date: 2015-12-30
HARBIN ENG UNIV
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Problems solved by technology

These calculation methods usually consider the case where the stiffness value of the boundary-constrained spring is uniformly distributed along the boundary, and cannot solve the more general case that the stiffness value of the boundary-constrained spring satisfies a non-uniform distribution along the boundary

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  • Method for analyzing vibration in structural surface of rectangular plate under non-uniform elastic constrained boundary condition
  • Method for analyzing vibration in structural surface of rectangular plate under non-uniform elastic constrained boundary condition
  • Method for analyzing vibration in structural surface of rectangular plate under non-uniform elastic constrained boundary condition

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Embodiment Construction

[0045] The present invention is described in more detail below in conjunction with accompanying drawing example:

[0046] to combine figure 1 ~4, the present invention comprises following flow process:

[0047] (1) The non-uniform in-plane constrained linear spring stiffness is expanded using Fourier series:

[0048] Let the length of a rectangular plate structure in the x-y plane of the Cartesian coordinate system be l x , with a width of l y , there are two sets of linear springs distributed on each boundary, which constrain the normal displacement and tangential displacement respectively. On the y=0 boundary, the normal and tangential linear spring stiffnesses are respectively denoted by k ny0 (x) and k py0 (x) to represent; at y=l y On the boundary, the normal and tangential linear spring stiffnesses are respectively denoted by k ny1 (x) and k py1 (x) to represent; on the x=0 boundary, the normal and tangential linear spring stiffnesses are respectively denoted by k...

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Abstract

The invention aims to provide a method for analyzing vibration in a structural surface of a rectangular plate under a non-uniform elastic constrained boundary condition. The method comprises the following steps: adopting Fourier series for unfolding the rigidity of a constraining linear spring in a non-uniform plane; adopting an energy principle for describing the vibration in the structural surface of the rectangular plate; applying a load in the plane at any acting angles to the structure of the rectangular plate; establishing the vibration displacement boundary smooth series in the structural surface of the rectangular plate; solving the system of vibration linear equations in the structural surfaces of any non-uniform boundary rectangular plates, thereby acquiring the vibration in the structural surface of the rectangular plate and forcing to respond and admit. Compared with the traditional methods, such as, the finite element method, and the like, the method provided by the invention has the advantage that the operation for the nodes is not required for the processing of the boundary condition in a non-uniform plane, so that the time for modeling and calculating is greatly saved. A rigidity distribution function of the spring can be adjusted for realizing any classic boundary conditions, uniform elastic constrained boundary conditions and non-uniform elastic constrained boundary conditions.

Description

technical field [0001] The invention relates to a vibration characteristic analysis method of a rectangular plate structure. Background technique [0002] Rectangular plate structures are widely used in many engineering fields, such as ship engineering, vehicle engineering, aerospace engineering and so on. Its vibration characteristics have been the focus of many researchers. Inside the plate structure, there are two different forms of vibration: bending vibration and in-plane vibration. Among them, the research on the bending vibration of plate structures started earlier, and the relevant literature is very rich. In recent years, some studies have shown that the in-plane vibration component of the structure also plays a very important role in the analysis of the energy transfer of composite structures. Therefore, the in-plane vibration analysis of rectangular plate structures has also attracted research interest in the field of structural dynamics. [0003] In order to ...

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Application Information

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IPC IPC(8): G06F17/14
Inventor 杜敬涛张羽飞刘杨许得水李文达
Owner HARBIN ENG UNIV
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