Exact solutions for the free in-plane vibrations of rectangular plates with arbitrary boundary conditions

2017 ◽  
Vol 130 ◽  
pp. 1-10 ◽  
Author(s):  
Yuansheng Zhou ◽  
Qingshan Wang ◽  
Dongyan Shi ◽  
Qian Liang ◽  
Zhongyu Zhang
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

A GENERALIZED ANALYTICAL APPROACH FOR THE BUCKLING ANALYSIS OF THIN RECTANGULAR PLATES WITH ARBITRARY BOUNDARY CONDITIONS

2011 ◽  
Vol 11 (01) ◽  
pp. 1-21 ◽  
Author(s):  
EUGENIO RUOCCO ◽  
VINCENZO MINUTOLO ◽  
STEFANO CIARAMELLA
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Analytical Approach ◽  
Elastic Stability ◽  
Rectangular Plates ◽  
The Finite Element Method ◽  
Dimensional Model ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Numerical Discretization

An analytical approach for studying the elastic stability of thin rectangular plates under arbitrary boundary conditions is presented. Because the solution is given in closed-form, the approach can be regarded as "exact" under the Kirchhoff–Love assumption. The proposed procedure allows us to obtain the buckling load and modal displacements that do not depend on the number of elements adopted in the numerical discretization using, say, the finite element method. Due to the fact that the longitudinal variation of the displacements is taken into account, the two-dimensional model established for the plate is considered "complete." Such an approach overcomes the shortcomings of conventional modeling presented in the literature. In order to demonstrate the generality of the proposed approach, several examples are prepared and the results obtained are compared with finite element and analytical solutions existing elsewhere.

scholarly journals Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
Dongyan Shi ◽  
Qingshan Wang ◽  
Xianjie Shi ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Practical Interest ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Solution Algorithms ◽  
Wide Range

A generalized Fourier series solution based on the first-order shear deformation theory is presented for the free vibrations of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions, a class of problem which is of practical interest and fundamental importance but rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the one displacement and two rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions are introduced to remove the potential discontinuities with the displacement components and its derivatives at the edges and to accelerate the convergence of series representations. All the series expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in the literatures and finite element method (FEM) data, and numerous new results for moderately thick rectangular plates with nonuniform thickness and elastic restraints are presented, which may serve as benchmark solution for future researches.

Vibration of Stiffened Plates

1964 ◽  
Vol 15 (3) ◽  
pp. 285-298 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
General Procedure ◽  
The Other ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions

SummaryThis paper presents a general procedure for calculating the natural frequencies of rectangular plates continuous over identical and equally spaced elastic beams which are simply-supported at their ends. Arbitrary boundary conditions are permissible on the other two edges of the plate. The results are compared with those obtained by using the orthotropic plate approximation for the system

scholarly journals Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-29 ◽  
Author(s):  
Guoyong Jin ◽  
Tiangui Ye ◽  
Shuangxia Shi
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Displacement Function ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Open Shells ◽  
Benchmark Solutions

This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.

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