A note on the vibrations of rectangular plates of variable thickness with two opposite simply supported edges and very general boundary conditions on the other two

1977 ◽  
Vol 50 (3) ◽  
pp. 445-454 ◽  
Author(s):  
C. Filipich ◽  
P.A.A. Laura ◽  
R.D. Santos
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
The Other ◽  
General Boundary ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Simply Supported ◽  
Plates Of Variable Thickness

Bending and Vibration of Plates of Variable Thickness

1976 ◽  
Vol 98 (1) ◽  
pp. 166-170 ◽  
Author(s):  
S. S. H. Chen
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
The Other ◽  
Polar Coordinates ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Plates Of Variable Thickness

The problem of bending and vibration of plates of variable thickness and arbitrary shapes and with mixed boundary conditions was solved by a modified energy method of the Rayleigh-Ritz type. General trial functions of deflection were obtained, one in Cartesian coordinates for rectangular plates and the other in polar coordinates for other shapes. The forced boundary conditions were satisfied approximately by introducing fixity factors which depended upon the prescribed conditions. Central deflections for circular plates subjected to static bending were within 0.2 percent of published results while they were within 1 percent for rectangular plates. The differences of natural frequencies of various rectangular plates were from 0.05 percent for simple, 2.9 percent for clamp, and up to 4.3 percent for free-free plates based on the published values.

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.

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

scholarly journals Three-dimensional free vibration of thick plates with general end conditions and resting on elastic foundations

2018 ◽  
Vol 38 (1) ◽  
pp. 110-121
Author(s):  
Zhuang Lin ◽  
Shuangxia Shi
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Three Dimensional ◽  
Series Representation ◽  
General Boundary ◽  
Geometrical Parameters ◽  
Penalty Function Method ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Elastic Foundations

This paper presents a three-dimensional formulation for the free vibrations of thick rectangular plates with general boundary conditions and resting on elastic foundations. The general boundary conditions are imposed by means of penalty function method. The displacements of the plates are expressed by a three-dimensional cosine series and some simple polynomial functions which introduced to ensure and accelerate the convergence of the series representation. All the unknown coefficients can be obtained by using the Rayleigh–Ritz method. Comparisons of the present results with those in available literature demonstrate the accuracy and reliability of the present formulation. Furthermore, parametric investigations are presented including the effects of boundary conditions, geometrical parameters, and elastic foundation.

Deflection and Moment Data for Rectangular Plates of Variable Thickness

1972 ◽  
Vol 39 (3) ◽  
pp. 814-815 ◽  
Author(s):  
P. Petrina ◽  
H. D. Conway
Keyword(s):  
Variable Thickness ◽  
Rectangular Plates ◽  
Direction Parallel ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Plates Of Variable Thickness

Numerical values of deflections and moments are given for uniformly loaded rectangular plates with a pair of opposite sides simply supported and the others either simply supported or clamped. The plates are tapered in a direction parallel to the simply supported sides. Data are given for two tapers and for plate aspect ratios equal to 1 (square plates), 1.5 and 2.

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