Mousa Rezaee, Reza Jahangiri,
Volume 14, Issue 13 (3-2015)
Abstract
In this study, static/dynamic instability and nonlinear vibrations of FG plates resting on elastic foundation under parametric forcing excitation, are investigated. Based on CPT, applying the von-Karman nonlinear strain–displacement relation and the Hamilton’s principle, the governing nonlinear coupled partial differential equations are derived. By considering six vibration modes, the Galerkin’s procedure is used to reduce the equations of motion to nonlinear Mathieu equations. In the absence of elastic foundation, the validity of the formulation for analyzing the static buckling, dynamic instability and nonlinear deflection is accomplished by comparing the results with those of the literature. Then in the presence of the foundation and by deriving the regions of dynamic instability, it is shown that as the parameters of the foundation increases, the natural frequency and the critical buckling load increase and the dynamic instability occurs at higher excitation frequencies. The frequency response equations in the steady-state condition are derived by applying the multiple scales method, and the parametric resonance is analyzed. Then the conditions of existence and stability of nontrivial solutions are discussed. Moreover, the effects of the system parameters, including excitation frequency, amplitude of excitation, foundation parameters and damping, on the nonlinear dynamics of the FG plate are investigated. Also it is shown that the presence of the foundation has a considerable influence on the resonance characteristic curves.
I. Ghoytasi, O. Rahmani,
Volume 19, Issue 12 (12-2019)
Abstract
In this paper, the effects of unified temperature loading and Winkler-Pasternak elastic foundation on the vibration of functionally graded curved nanobeam have been studied. The proposed model is based on the modified couple stress theory and the Timoshenko beam model. The continuous distribution of material along the thickness of functionally graded curved nanobeam is achieved by changing the gradient index in the volume fraction. The governing equations and related boundary conditions are obtained using the Hamilton principle. By analyzing the quantitative and qualitative results in the tables and figures, influences of geometrical and thermo-physical parameters such as gradient index, aspect ratio, unified temperature difference, the ratio of thickness to length scale parameter and arc angle of functionally graded curved nanobeam on the natural frequency for different vibration mode have been interpreted. There is an excellent agreement between the present results and the results of the previous works. Applied temperature loading increases the sensitivity of the natural frequency to the changes in the aforementioned parameters and also increases the range of its changes. Also, applying the Pasternak elastic foundation changes the behavior of the natural frequency to the temperature changes.
