scholarly journals A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

2016 ◽  
Vol 40 (21-22) ◽  
pp. 9228-9253 ◽  
Author(s):  
Qingshan Wang ◽  
Dongyan Shi ◽  
Qian Liang ◽  
Fazl e Ahad
Keyword(s):  
Boundary Conditions ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Plane Vibration

Free In-Plane Vibration Analysis of Annular Plates with General Boundary Conditions

2013 ◽  
Vol 572 ◽  
pp. 189-192
Author(s):  
Dong Yan Shi ◽  
Xian Jie Shi ◽  
Wen L. Li ◽  
Zheng Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Current Method ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Series Solutions ◽  
Plane Vibration ◽  
Annular Plates ◽  
Special Cases

An analytical method is derived for the free in-plane vibration analysis of annular plates with general boundary conditions. Under this framework, all the classical homogeneous boundary conditions can be treated as the special cases when the stiffness for each restraining springs is equal to either zero or infinity. The improved Fourier series solutions for the in-plane vibrations are obtained by employing the Rayleigh-Ritz method. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

Flexural Vibration Response of Beams With General Boundary Conditions: A Transfer Matrix Approach

1991 ◽  
Author(s):  
T. Önsay
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Response ◽  
General Boundary ◽  
Phase Variable ◽  
General Boundary Conditions ◽  
Transfer Matrices ◽  
Analytical Results

Abstract The wave-mode representation is utilized to obtain a more efficient form to the conventional transfer matrix method for bending vibrations of beams. The proposed improvement is based on a phase-variable canonical state representation of the equation governing the time-harmonic flexural vibrations of a beam. Transfer matrices are obtained for external forces, step-change of beam properties, intermediate supports and for boundaries. The transfer matrices are utilized to obtain the vibration response of a point-excited single-span beam with general boundary conditions. The general characteristic equation and the transfer mobility of a single-span beam are determined. The application of the analytical results are demonstrated on physical structures with different boundary conditions. A hybrid model is developed to incorporate measured impedance of nonideal boundaries into the transfer matrix method. The analytical results are found to be in excellent agreement with experimental measurements.

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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