Vibration Analysis of Arbitrarily Shaped Sandwich Plates via Ritz Method

2001 ◽  
Vol 8 (2) ◽  
pp. 101-118
Author(s):  
C. M. Wang, K. K. Ang, L. Yang, E. Wat
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Sandwich Plates

Vibration Analysis of Arbitrarily Shaped Sandwich Plates via Ritz Method

2001 ◽  
Vol 8 (2) ◽  
pp. 101-118 ◽  
Author(s):  
C. M. Wang ◽  
K. K. Ang ◽  
L. Yang ◽  
E. Watanabe
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Sandwich Plates

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

Vibration analysis of rotating toroidal shell by the Rayleigh-Ritz method and Fourier series

2018 ◽  
Vol 173 ◽  
pp. 870-891 ◽  
Author(s):  
Ivo Senjanović ◽  
Neven Alujević ◽  
Ivan Ćatipović ◽  
Damjan Čakmak ◽  
Nikola Vladimir
Keyword(s):  
Fourier Series ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Toroidal Shell

Vibration Analysis of Laminated Composite Rectangular Plates With General Boundary Conditions

2018 ◽  
Author(s):  
Yu Fu ◽  
Jianjun Yao ◽  
Zhenshuai Wan ◽  
Gang Zhao
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Geometric Parameters ◽  
General Boundary ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Benchmark Solutions

In this investigation, the free vibration analysis of laminated composite rectangular plates with general boundary conditions is performed with a modified Fourier series method. Vibration characteristics of the plates have been obtained via an energy function represented in the general coordinates, in which the displacement and rotation in each direction is described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate any possible jumps and boundary discontinuities. All the expansion coefficients are then treated as the generalized coordinates and determined by Rayleigh-Ritz method. The convergence and reliability of the current method are verified by comparing with the results in the literature and those of Finite Element Analysis. The effects of boundary conditions and geometric parameters on the frequencies are discussed as well. Finally, numerous new results for laminated composite rectangular plates with different geometric parameters are presented for various boundary conditions, which may serve as benchmark solutions for future research.

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