Rectangular plate vibration mode calculation method based on spectrum finite element
A vibration mode and calculation method technology, applied in calculation, design optimization/simulation, special data processing applications, etc., can solve problems that have not considered other boundary conditions of rectangular plates, and the accuracy needs to be improved.
Active Publication Date: 2017-05-31
HUNAN UNIV OF SCI & TECH
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Gang Wang conducted a series of studies on the free vibration problem and vibration mode calculation problem of the plate, mainly using the Kantorovich–Krylov variational method for the internal vibration mode of the rectangular plate and the bending vibration problem. The finite element method studies the free vibration of stepped plates, but it does not consider the influence of shear angles in two directions at any point in the plate during the calculation process, and the calculation accuracy for relatively thick plates needs to be improved
M. Boscolo used the first-order shear theory to obtain the dynamic stiffness element of the plate to accurately analyze the free vibration of the rectangular plate. However, this method only considers the case where a certain opposite side of the rectangular plate is a simply supported boundary condition, and has not considered the application to the rectangular plate. Cases with other boundary conditions
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[0241] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0242] A method for calculating the vibration mode of a rectangular plate based on spectral finite elements, comprising the following steps:
[0243] Step 1: Obtain the boundary value problem model of plate vibration based on the principle of energy function variation, and then obtain the free vibration equations in two directions based on the variable separation method.
[0244] The specific steps are
[0245] Establish a rectangular plate Cartesian coordinate system (x, y, z), and define the displacement multivariate functions u(x, y, t), v(x, y, t), w(x, y,t) as follows:
[0246] u(x,y,t)=zθ y (x,y,t);
[0247] v(x,y,t)=-zθ x (x,y,t);
[0248] w(x,y,t)=w 0 (x,y,t);
[0249] where w 0 (x, y, t) represents the vibration amplitude of the plate (x, y) position at time t in the z direction, θ x Indicates the rotation angle of the plate (x,y) posit...
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The invention discloses a rectangular plate vibration mode calculation method based on the spectrum finite element. The method comprises the following steps that a plate vibration boundary value problem module is obtained on the basis of the energy function variation principle, and free vibration equations of two directions are obtained on the basis of the variable separation method; the boundary conditions of the two directions of the rectangular plate are determined, the vibration frequencies and the vibration modes are calculated by mutual iteration of different directions under the preset modal order, and the calculation is stopped until the error of the vibration frequencies, obtained by calculation, of the two directions is in a certain designated range; the finally obtained vibration modes of the two directions are used for overlaying to obtain the rectangular plate vibration mode. Calculation of the plate vibration modes is performed aiming at various combined boundary conditions, the influences of the rotation corners of any position of the two directions in the plate on the calculation effect of the plate vibration modes is considered, the vibration equation with the amplitude and the two rotation corners taken as the variables is obtained, the calculated result is more accurate, and the calculation method has the advantages that the practicability is wide and the application is convenient.
Description
technical field [0001] The invention relates to a method for calculating the vibration mode of a rectangular plate based on spectrum finite elements. Background technique [0002] Plate structures play a very important role in engineering applications, and are widely used in aviation, civil engineering, and electronic engineering. Vibration analysis of plate structure is the key to engineering application design, and also the basis and important part of vibration response analysis. [0003] Aiming at the problem of free vibration mode calculation of plate structure, many scholars have carried out fruitful research. Y. Xiang calculated the vibration frequency of a stepped rectangular Mindlin plate with simply supported boundary conditions on one side using the domain decomposition calculation method, and obtained its analytical solution. Yufeng Xing used the method of direct separation of variables to obtain the solution of the free vibration closed-loop form of the rectang...
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Login to View More IPC IPC(8): G06F17/50
CPCG06F30/23
Inventor 蒋勉伍济钢王钢李学军王广斌林京张文安
Owner HUNAN UNIV OF SCI & TECH