Free Vibration of Anisotropic Rectangular Plates by General Analytical Method

HUANG Yan; LEI Yong-jun; SHEN Hui-jun

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HUANG Yan, LEI Yong-jun, SHEN Hui-jun. Free Vibration of Anisotropic Rectangular Plates by General Analytical Method[J]. Applied Mathematics and Mechanics, 2006, 27(4): 411-416.

Citation:

HUANG Yan, LEI Yong-jun, SHEN Hui-jun. Free Vibration of Anisotropic Rectangular Plates by General Analytical Method[J]. Applied Mathematics and Mechanics, 2006, 27(4): 411-416.

Citation:

HUANG Yan, LEI Yong-jun, SHEN Hui-jun. Free Vibration of Anisotropic Rectangular Plates by General Analytical Method[J]. Applied Mathematics and Mechanics, 2006, 27(4): 411-416.

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Free Vibration of Anisotropic Rectangular Plates by General Analytical Method

College of Aerospace and Material Engineering, National University of Defense Technology, Changsha 410073, P. R. China

Received Date: 2004-07-30
Rev Recd Date: 2005-10-25
Publish Date: 2006-04-15

Abstract

Abstract

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration,a general analytical solution was established.This general solution composed of the composite solutions made by trigonometric function and hyperbolic function,can satisfy the problem of arbitrary boundary conditions along four edges.The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners.Consequently,this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately.The integral constants can be determined by boundary conditions of four edges and four corners.Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero.For example,a composite symmetric angle ply laminated plate with four edges clamped was calculated and discussed.
- anisotropic plate,
- free vibration,
- general analytical method,
- frequency,
- mode shape

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References(15)

References

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