Vibration analysis of rectangular plates with side cracks via the Ritz method

2009 ◽  
Vol 323 (3-5) ◽  
pp. 974-988 ◽  
Author(s):  
C.S. Huang ◽  
A.W. Leissa
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Rectangular Plates

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.

Vibration Analysis of Damaged Rectangular Plates with General Elastic Boundary Supports

2011 ◽  
Vol 368-373 ◽  
pp. 2189-2193
Author(s):  
Fu Hou Xu ◽  
Yu Xiang Zhang ◽  
Jia Zhao Chen ◽  
Jin Biao Xu ◽  
Yun Zhou
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Third Order ◽  
Characteristic Equations ◽  
Numerical Examples ◽  
First Order ◽  
The Third ◽  
Elastic Boundary ◽  
Nature Frequency

This paper proposed a method to calculate the nature frequencies of generally supported plate with hole. The boundary of plate is considered as the combination of rotational springs and translational springs. The generally characteristic equations of generally supported plate with damage can be derived using Rayleigh-Ritz method. The nature frequencies of damaged plate can be obtained by solving the generally characteristic equations. The calculated results by proposed method were compared with that of FEM (finite element method) and analytical solutions. The compared results demonstrated that the proposed method is accurate and effective. Numerical examples are presented to analyze the effect of damage on the plate under different kinds of elastic restraint. The results suggest that: the effect of damage is little to the first order nature frequency and is relative large to the third order nature frequency when the rotational restraints are weak; the effect on the first order nature frequency rises but the effect on the third order nature frequency fall as the rotational restraints increase.

scholarly journals Influence of boundary conditions on three-dimensional vibration characteristics of thick rectangular plates

2020 ◽  
Vol 103 (4) ◽  
pp. 003685042096954
Author(s):  
Yufei Zhang ◽  
Jingtao Du
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Design Procedure ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Element Analysis ◽  
Elastically Restrained

Vibration analysis of the classical elastic structures is not only essential for the study of vibration reduction by predicting the dynamic behavior, but also important to ensure a reliable, safe, and lasting structural performance through the proper design procedure. In this paper, the influence of boundary conditions on the free and forced three-dimensional vibration analysis of thick rectangular plates has been performed using the improved Fourier series method. For the elastically restrained thick rectangular plate, the three-dimensional improved Fourier series displacement forms are used to model the vibration field. The energy formula is employed to describe the three-dimensional dynamics of the plate. All the unknown Fourier series coefficients are then solved by the Rayleigh-Ritz method. In order to validate the proposed model, several numerical examples are provided and compared against the results from the literature and Finite Element Analysis (FEA). In addition, the effects of the boundary restraining spring stiffness and the thickness ratios of thick rectangular plates are analyzed under elastically restrained boundary conditions to develop an in-depth understanding of the three-dimensional vibration characteristics of thick rectangular plates.

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