scholarly journals A Semianalytical Three-Dimensional Elasticity Solution for Vibrations of Orthotropic Plates with Arbitrary Boundary Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Jie Cui ◽  
Zichao Li ◽  
Renchuan Ye ◽  
Wenan Jiang ◽  
Shenghui Tao
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Three Dimensional ◽  
Displacement Function ◽  
Elasticity Solution ◽  
Orthotropic Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
3D Elasticity ◽  
Three Dimensional Elasticity

A semianalytical three-dimensional (3D) elasticity solution for the vibration of the orthotropic plate is presented under arbitrary boundary conditions. Three-dimensional (3D) elasticity theory provides the theoretical support for the energy function of orthotropic plates. The orthotropic plates which have the arbitrary boundary condition are realized by the way of arranging three sets of linear springs at the edges. With the aim of eliminating the nonsmooth phenomenon at the edges, the admissible displacement function of an orthotropic plate is expressed with a modified Fourier series solution. Under this framework, a change that occurs on the boundary conditions only needs to modify the boundary parameters of the orthotropic plate, without the need for new derivation, thus greatly saving the modeling time. The convergence and accuracy of the proposed method are better than those of the published literature. Lastly, the new vibration results and parametric research of thick orthotropic plates as well as the geometric parameter are also presented.

scholarly journals Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huimin Liu ◽  
Fanming Liu ◽  
Xin Jing ◽  
Zhenpeng Wang ◽  
Linlin Xia
Keyword(s):  
Boundary Conditions ◽  
Admissible Function ◽  
Three Dimensional ◽  
Future Research ◽  
Pasternak Foundation ◽  
Arbitrary Boundary ◽  
Thick Plates ◽  
Arbitrary Boundary Conditions ◽  
Ritz Procedure ◽  
Three Dimensional Elasticity

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

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.

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

Static and Dynamic Analysis of Annular Sector Plates Subjected to Arbitrary Boundary Conditions

2014 ◽  
Vol 624 ◽  
pp. 240-244
Author(s):  
Kai Peng Zhang ◽  
Cheng Yang ◽  
Han Wu
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Current Method ◽  
Displacement Function ◽  
Current Approach ◽  
Arbitrary Boundary ◽  
Static And Dynamic Analysis ◽  
Arbitrary Boundary Conditions ◽  
Annular Sector

In this investigation, an improved Fourier series method (IFSM) is employed to predict the static and dynamic characteristics of annular sector plates with arbitrary boundary conditions. Regardless of boundary supports, the displacement function is invariantly expressed as a modified two-dimensional Fourier series containing sine and cosine function. It is capable of dealing with the possible discontinuities at elastic boundary edges. The unknown Fourier coefficients are treated as generalized coordinates, and determined using Rayleigh-Ritz method. Unlike most of the existing solution techniques, the current approach can be universally applied to a variety of edge restraints including all classical cases and their combinations. The accuracy and reliability of the current method are fully illustrated through all the numerical examples.

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