Free vibration analysis of angle-ply symmetric laminated plates with free boundary conditions by the discrete singular convolution

2017 ◽  
Vol 170 ◽  
pp. 91-102 ◽  
Author(s):  
Xinwei Wang
Keyword(s):  
Free Boundary ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Laminated Plates ◽  
Free Boundary Conditions ◽  
Discrete Singular Convolution

DISCRETE SINGULAR CONVOLUTION (DSC) FOR FREE VIBRATION ANALYSIS OF CONICAL SHELLS WITH VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (01) ◽  
pp. 81-108 ◽  
Author(s):  
ÖMER CIVALEK
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shell Theory ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Conical Shells ◽  
Various Boundary Conditions ◽  
Discrete Singular Convolution ◽  
Thin Shell Theory

This paper gives a relatively novel computational approach, the discrete singular convolution (DSC) algorithm, for the free vibration analysis of isotropic and orthotropic conical shells with different boundary conditions. The governing differential equations of vibration of the shell are formulated using Love's first approximation classical thin shell theory. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. Typical numerical results are presented illustrating the effect of various geometric and material parameters. The influence of boundary conditions on the frequency characteristics is also discussed. The obtained results are in excellent agreement with those in the literature.

Free vibration analysis of rectangular and annular Mindlin plates with undamaged and damaged boundaries by the spectral collocation method

2011 ◽  
Vol 18 (11) ◽  
pp. 1722-1736 ◽  
Author(s):  
Ma’en S Sari ◽  
Eric A Butcher
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Collocation Method ◽  
Vibration Analysis ◽  
Natural Vibration ◽  
Numerical Technique ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Grid Points ◽  
Matrix Vector

The objective of this paper is the development of a new numerical technique for the free vibration analysis of isotropic rectangular and annular Mindlin plates with damaged boundaries. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of Mindlin plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational and torsional springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged Mindlin plate indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for structural health monitoring of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

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