Three-dimensional exact solution for the free vibration of thick functionally graded annular sector plates with arbitrary boundary conditions

2019 ◽  
Vol 159 ◽  
pp. 418-436 ◽  
Author(s):  
Jing Zhao ◽  
Yongkang Zhang ◽  
Kwangnam Choe ◽  
Xiaofei Qu ◽  
Ailun Wang ◽  
...  
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Annular Sector

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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