scholarly journals A semi-analytical method for vibration analysis of thin spherical shells with elastic boundary conditions

2017 ◽  
Vol 19 (4) ◽  
pp. 2312-2330 ◽  
Author(s):  
Meixia Chen ◽  
Kun Xie ◽  
Zuhui Li
Keyword(s):  
Boundary Conditions ◽  
Analytical Method ◽  
Vibration Analysis ◽  
Spherical Shells ◽  
Elastic Boundary ◽  
Elastic Boundary Conditions

scholarly journals A Hybrid Finite Element-Fourier Spectral Method for Vibration Analysis of Structures with Elastic Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Wan-You Li ◽  
Binglin Lv ◽  
Huajiang Ouyang ◽  
Jingtao Du ◽  
Haijun Zhou ◽  
...  
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Spectral Method ◽  
Hybrid Method ◽  
Vibration Analysis ◽  
Present Method ◽  
Fourier Spectral Method ◽  
Elastic Boundary ◽  
Elastic Boundary Conditions

A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM) and the applicability of the finite element method (FEM), is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.

Free vibration analysis of rectangular plates with arbitrary elastic boundary conditions

2021 ◽  
Vol 263 (5) ◽  
pp. 1891-1898
Author(s):  
Zhenshuai Wan
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Different Boundary Conditions ◽  
Elastic Boundary ◽  
Fourier Series Method ◽  
The Matrix ◽  
Elastic Boundary Conditions

boundary conditions are In this paper, an improved Fourier series method is presented for the free vibration analysis of rectangular plates with arbitrary elastic conditions. The stiffness value of the restraining springs is determined as required to simulate the arbitrary elastic boundary conditions. The exact solution of plates with arbitrary elastic boundary conditions is solved by the introduced supplementary func-tions. The matrix eigenvalue equation of plates is derived by using boundary conditions and the governing equations. Compared with exist methods, the presented method can be easily applied to most of plate vibration problems with different boundary conditions. To validate the accuracy of the presented method, numerical simulations with different boundary conditions are presented.presented.

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