Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method

2011 ◽  
Vol 53 (7) ◽  
pp. 494-504 ◽  
Author(s):  
L.H. Wu ◽  
Y. Lu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Elastic Edge

Free Vibration Analysis of Rectangular Plates with Nonuniform Lateral Elastic Edge Support

1993 ◽  
Vol 60 (4) ◽  
pp. 998-1003 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Elastic Supports ◽  
Proper Frequency ◽  
Elastic Edge ◽  
Edge Stiffness

The method of superposition is utilized to obtain a solution for the free vibration of thin rectangular plates resting on non-uniform lateral elastic edge supports. The stiffness of the elastic supports may have any desired distribution along the edges, including discontinuities and local concentrations. Convergence is found to be rapid. Graphical results are plotted for square plates in order to verify that proper frequency limits are approached as the edge stiffness approach limits of zero and infinity. Results are tabulated for square and nonsquare plates in order that other researchers will have data against which they can compare their results.

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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