Analysis of Nonlinear Vibration of Magneto-Electro-Elastic Plate on Elastic Foundation Based on High-Order Shear Deformation

2021 ◽  
pp. 114149
Author(s):  
L.L. Xu ◽  
C.C. Kang ◽  
Y.F. Zheng ◽  
C.P. Chen
Keyword(s):  
Nonlinear Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Elastic Plate ◽  
High Order ◽  
Plate On Elastic Foundation

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment

2018 ◽  
Vol 22 (4) ◽  
pp. 1157-1183 ◽  
Author(s):  
Nguyen Thi Phuong ◽  
Vu Hoai Nam ◽  
Dang Thuy Dong
Keyword(s):  
Nonlinear Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Thermal Environment ◽  
Geometrical Nonlinearity ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
First Order ◽  
Spherical Caps

A semi-analytical approach to investigate the nonlinear vibration axisymmetric analysis of functionally graded sandwich shallow spherical caps under external pressure resting on elastic foundation in thermal environment is presented. The governing equations are derived by using the first-order shear deformation theory taking into account von Karman geometrical nonlinearity and Pasternak’s two-parameter elastic foundation. The motion equations are determined by Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. Results of nonlinear dynamic responses show the effects of foundation, material, geometric parameters, and temperature change on the nonlinear vibration of shells.

On the Vibration of an Elastic Plate on an Elastic Foundation

1967 ◽  
Vol 42 (5) ◽  
pp. 1202-1202
Author(s):  
David H. Y. Yen ◽  
S. C. Tang
Keyword(s):  
Elastic Foundation ◽  
Elastic Plate
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