Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions

2014 ◽  
Vol 108 ◽  
pp. 565-577 ◽  
Author(s):  
Guoyong Jin ◽  
Zhu Su ◽  
Shuangxia Shi ◽  
Tiangui Ye ◽  
Siyang Gao
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Functionally Graded ◽  
General Boundary ◽  
Rectangular Plates ◽  
General Boundary Conditions

scholarly journals Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Shi ◽  
Shuai Zha ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
Volume Distribution ◽  
General Boundary Conditions

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and Rayleigh-Ritz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

scholarly journals Three-dimensional free vibration of thick plates with general end conditions and resting on elastic foundations

2018 ◽  
Vol 38 (1) ◽  
pp. 110-121
Author(s):  
Zhuang Lin ◽  
Shuangxia Shi
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Three Dimensional ◽  
Series Representation ◽  
General Boundary ◽  
Geometrical Parameters ◽  
Penalty Function Method ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Elastic Foundations

This paper presents a three-dimensional formulation for the free vibrations of thick rectangular plates with general boundary conditions and resting on elastic foundations. The general boundary conditions are imposed by means of penalty function method. The displacements of the plates are expressed by a three-dimensional cosine series and some simple polynomial functions which introduced to ensure and accelerate the convergence of the series representation. All the unknown coefficients can be obtained by using the Rayleigh–Ritz method. Comparisons of the present results with those in available literature demonstrate the accuracy and reliability of the present formulation. Furthermore, parametric investigations are presented including the effects of boundary conditions, geometrical parameters, and elastic foundation.

Sign in / Sign up

Export Citation Format

Share Document