A Method for In-plane Vibration Analysis of Rectangular Slab Structures with Inhomogeneous Elastic Constraint Boundary Conditions
A technology of elastic constraints and boundary conditions, applied in complex mathematical operations, etc., can solve problems such as inability to solve boundary-constrained springs to satisfy non-uniform distribution, and achieve the effects of saving modeling and calculation time, fast convergence speed, and high calculation accuracy.
Active Publication Date: 2017-11-28
HARBIN ENG UNIV
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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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[0045] The present invention is described in more detail below in conjunction with accompanying drawing example:
[0046] 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 groups 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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The object of the present invention is to provide a method for in-plane vibration analysis of a rectangular plate structure with inhomogeneous elastic constraint boundary conditions, including the following steps: expand the linear spring stiffness of the inhomogeneous in-plane constraint using Fourier series, and use the energy principle to describe the rectangular plate structure In-plane vibration, apply an in-plane load of any action angle to the rectangular plate structure, construct the smooth series of vibration displacement boundary in the rectangular plate structure, and solve the linear equations of the in-plane vibration of the rectangular plate structure with any non-uniform boundary, so as to obtain the rectangular plate structure surface Internal vibration forced response admittance. Compared with traditional methods such as finite elements, the present invention does not need to operate nodes for the processing of boundary conditions in a non-uniform plane, thereby greatly saving modeling and calculation time; by adjusting the stiffness distribution function of the spring, any classical boundary conditions, Uniform elastic constrained boundary conditions as well as 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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IPC IPC(8): G06F17/14
Inventor 杜敬涛张羽飞刘杨许得水李文达
Owner HARBIN ENG UNIV