A generalized model for predicting the sound transmission properties of generally orthotropic plates with arbitrary boundary conditions

1995 ◽  
Vol 97 (2) ◽  
pp. 1099-1112 ◽  
Author(s):  
Roland Woodcock ◽  
Jean Nicolas
Keyword(s):  
Boundary Conditions ◽  
Sound Transmission ◽  
Orthotropic Plates ◽  
Arbitrary Boundary ◽  
Generalized Model ◽  
Arbitrary Boundary Conditions ◽  
Transmission Properties

scholarly journals An Optimization Method for Maximizing the Low Frequency Sound Insulation of Plate Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dayi Ou
Keyword(s):  
Genetic Algorithm ◽  
Boundary Conditions ◽  
Low Frequency ◽  
Sound Transmission ◽  
Sound Insulation ◽  
Plate Structures ◽  
Arbitrary Boundary ◽  
Frequency Sound ◽  
Arbitrary Boundary Conditions ◽  
Element Method

A combined approach based on finite element method, boundary element method, and genetic algorithm (FEM-BEM-GA) is proposed for optimizing the low frequency sound (LFS) insulation performance of plate structures. This approach can identify the optimal structural parameters (especially concerning the effects of arbitrary boundary conditions) so as to maximize the structural overall LFS insulation. The basic ideas of this approach are as follows: (1) the sound transmission loss (TL) analysis of a plate with arbitrary boundary conditions is conducted by the coupled FEM-BEM method; (2) the single-number rating method (such as low frequency sound transmission class) is used to assess the plate’s overall LFS insulation; and (3) the genetic algorithm (GA) is employed for searching the optimal solutions of the multiple-parameter optimization problem. The proposed approach is subsequently illustrated by numerical studies. The results show the effectiveness of consideration of the effects of boundary condition in the plate’s LFS insulation optimization and demonstrate the feasibility and effectiveness of this approach as a structure design tool.

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 A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

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.

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