Nonlinear dynamic analysis of sandwich S-FGM plate resting on Pasternak foundation under thermal environment. (English) Zbl 1472.74093
Summary: In the present study, stress-function Galerkin (SFG) method is employed to investigate the dynamic characteristics of a new sigmoid law based sandwich functionally graded plate (S-FGM) plates resting of Pasternak elastic foundation in the thermal environment. For modified sigmoid law, a new temperature profile is derived considering 1D steady state heat conduction equation. The Hamiltonian formulation is done to derive governing equations and nonlinearity, due to Von- Karman strains, is worked out using Airy’s function in conjunction with Galerkin’s method. The time and frequency domain analysis is then performed using a numerical integration scheme and harmonic balance method, respectively. The nonlinear rise in temperature is considered across the thickness due to the temperature difference between the top and the bottom surface of the simply supported plate with immovable edges. Wide-Ranging parametric studies for, linear and nonlinear, frequency and time domain analysis have been performed by taking into consideration the effect of thickness ratio, inhomogeneity parameter, thermal load, and foundation parameter for various configurations of the sandwich plates. Poincaré maps, phase-plane plots and time responses are demonstrated to study the nonlinear dynamics behavior of sandwich S-FGM plate under harmonic excitation. The variation of aspect ratios shows the route to chaos. With the Winkler foundation, the response is chaotic but becomes weakly chaotic with the introduction of the Pasternak type foundation. The dynamic response clearly shows the route to chaos with the varying thermal load from \(\Delta T = 0-600\) K. It is observed that the periodicity of the plate behavior is primarily affected by considering different configurations of the sandwich S-FGM plate. The computed results and observations can be utilized as a validation study for future examination for sandwich S-FGM plates.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
| 74H65 | Chaotic behavior of solutions to dynamical problems in solid mechanics |
| 74K20 | Plates |
| 74E30 | Composite and mixture properties |
| 74F05 | Thermal effects in solid mechanics |
Keywords:
sigmoid law; von Karman strain; Poincaré map; route to chaos; Airy function; stress-function Galerkin method; harmonic balance methodReferences:
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