A complete analogical study on the dynamic stability analysis of isotropic functionally graded plates subjected to lateral stochastic loads

2015 ◽  
Vol 226 (7) ◽  
pp. 2347-2363 ◽  
Author(s):  
A. Asnafi ◽  
M. Abedi
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Stochastic Loads

A comparison between the dynamic stability of three types of nonlinear orthotropic functionally graded plates under random lateral loads

2015 ◽  
Vol 23 (15) ◽  
pp. 2520-2537 ◽  
Author(s):  
A Asnafi ◽  
M Abedi
Keyword(s):  
Dynamic Stability ◽  
Three Dimensional ◽  
Mean Value ◽  
Functionally Graded ◽  
Kolmogorov Equation ◽  
Lateral Loads ◽  
Functionally Graded Plates ◽  
The Mean ◽  
Stochastic Loads ◽  
Stable Zone

In this manuscript, the dynamic stability and bifurcation occurrence for three famous types of plates including orthotropic sigmoid, power-law and exponential functionally graded plates under lateral stochastic loads are studied. Due to randomness, the behavior and analysis are not conventional deterministic investigation. So, the dynamic stability zone and border curves of bifurcation are evaluated using probability density function of the response. The latter is computed from a completely exact solution of the Fokker Planck Kolmogorov equation. The three dimensional dynamic stable zone and the border surfaces of bifurcation are obtained as a function of material parameter, in-plane forces and the mean value of lateral load. To generalize the results, all the parameters are transformed to some proper non-dimensional variables and then the effects of all prescribed parameters on the dynamic stability are completely discussed and compared. The comparison is done between the plates with themselves and also the corresponding homogenous plate. Finally the results are validated by the bifurcation diagrams of non dimensional deflection of plates that are obtained directly and numerically from the governing equations of plates.

Dynamic Stability Analysis of Functionally Graded Plates Subjected to Complex Loads

2014 ◽  
Vol 578-579 ◽  
pp. 679-686 ◽  
Author(s):  
Sheng Fei Yang ◽  
Hao Chen ◽  
Chun Ran
Keyword(s):  
Least Squares ◽  
Dynamic Stability ◽  
Differential Quadrature Method ◽  
Instability Region ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Moving Least Squares ◽  
Quadrature Method ◽  
Thickness Direction ◽  
Functionally Graded Plates

The paper investigates the dynamic stability of thick functionally graded plates subjected to aero-thermo-mechanical loads, using the moving least squares differential quadrature method. Temperature field is assumed to be a uniform distribution over the plate plane, and varied in the thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction in the simple power law manner. The equilibrium equations governing the dynamic stability of the plate are derived by the Hamilton’s principle, then these equations are discretized by the moving least squares differential quadrature method. The boundaries of the instability region are obtained using the principle of Bolotin’s method and are conveniently represented in the non-dimensional excitation frequency to load amplitude plane. The influence of various factors such as gradient index, temperature, mechanical and aerodynamic loads, thickness and aspect ratios, as well as the boundary conditions on the dynamic instability region are carefully studied.

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