A unified approach for predicting sound radiation from baffled rectangular plates with arbitrary boundary conditions

2010 ◽  
Vol 329 (25) ◽  
pp. 5307-5320 ◽  
Author(s):  
Xuefeng Zhang ◽  
Wen L. Li
Keyword(s):  
Boundary Conditions ◽  
Sound Radiation ◽  
Rectangular Plates ◽  
Unified Approach ◽  
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.

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

2020 ◽  
Vol 20 (05) ◽  
pp. 2050068 ◽  
Author(s):  
Zhengmin Hu ◽  
Kai Zhou ◽  
Yong Chen
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Arbitrary Boundary Conditions ◽  
Porosity Coefficient

In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified Fourier series method. It is assumed that a total of three types of porosity distributions are considered in the present study. The material parameters are determined according to the porosity coefficient used to denote the size of pores in the plate. The governing equations of the FGP plate are derived by utilizing the Hamilton’s principle on the basis of the first-order deformation theory (FSDT). Each displacement component of the FGP plate is expanded as the Fourier cosine series combined with auxiliary polynomial functions introduced to enhance the convergence rate of the series expansions. The acoustic response of the FGP plate due to a concentrated harmonic load is calculated by evaluating the Rayleigh integral. Good agreements are attained by comparing the present results with those in available literatures, which show the accuracy and versatility of the developed method in this paper. Finally, the influences of the porosity distribution type, porosity coefficient, boundary condition and elastic foundation on the sound radiation of the FGP plate are analyzed in detail.

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.

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