NONLINEAR VIBRATIONS OF SANDWICH FG PLATES RESTING ON NONLINEAR PASTERNAK FOUNDATION UNDER PRIMARY RESONANCE EXCITATION USING MODIFIED FSDT

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REZAEE MOUSA; JAHANGIRI REZA

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Journal: Modares Mechanical Engineering Year:2015 | Volume:14 | Issue:15 Page(s): 186-198

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Title

NONLINEAR VIBRATIONS OF SANDWICH FG PLATES RESTING ON NONLINEAR PASTERNAK FOUNDATION UNDER PRIMARY RESONANCE EXCITATION USING MODIFIED FSDT

Author(s)

REZAEE MOUSA | JAHANGIRI REZA | Issue Writer Certificate

Keywords

SANDWICH FG PLATEQ2

NONLINEAR PASTERNAK FOUNDATIONQ2

TRANSVERSE FORCING EXCITATIONQ2

MULTIPLE SCALE METHODQ2

SADDLE NODE BIFURCATIONQ2

Abstract

In this study, the nonlinear vibration of a SANDWICH FG PLATE resting on a NONLINEAR PASTERNAK FOUNDATION which is simultaneously subjected to transverse harmonic forcing excitation and inplane static force is investigated. Based on the Modified First-Order Shear Deformation Theory (FSDT), applying the von-Karman nonlinear strain–displacement relation and the Hamilton’s principle, the governing nonlinear coupled partial differential equations are derived. Then, the Galerkin’s procedure is used to reduce the equations of motion to nonlinear ordinary differential equations. In the absence of foundation, the validity of the formulation for analyzing the modified shear correction factors for shear stresses is accomplished by comparing the results with those reported in the literature. By applying the multiple scales method and considering the second order nonlinear approximation of solution, the primary resonance of the system under the TRANSVERSE FORCING EXCITATION is analyzed. Under the steady-state condition, the frequency response, the force-response and the damping-response equations are derived. Then the conditions of existence and stability of multiple coexisting non-trivial solutions for amplitude of the responses are discussed and the SADDLE NODE BIFURCATION points of the characteristic curves are derived. It is shown that, the variation of the system parameters in the resonance boundary may cause the jump phenomenon. Moreover, the effects of the system parameters including, excitation frequency, foundation parameters, damping, and amplitude of the harmonic and inplane forces on the system nonlinear dynamics are investigated. Also it is shown that the presence of the foundation has a considerable influence on the resonance characteristic curves.

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APA: Copy

REZAEE, MOUSA, & JAHANGIRI, REZA. (2015). NONLINEAR VIBRATIONS OF SANDWICH FG PLATES RESTING ON NONLINEAR PASTERNAK FOUNDATION UNDER PRIMARY RESONANCE EXCITATION USING MODIFIED FSDT. MODARES MECHANICAL ENGINEERING, 14(15), 186-198. SID. https://sid.ir/paper/177683/en

Vancouver: Copy

REZAEE MOUSA, JAHANGIRI REZA. NONLINEAR VIBRATIONS OF SANDWICH FG PLATES RESTING ON NONLINEAR PASTERNAK FOUNDATION UNDER PRIMARY RESONANCE EXCITATION USING MODIFIED FSDT. MODARES MECHANICAL ENGINEERING[Internet]. 2015;14(15):186-198. Available from: https://sid.ir/paper/177683/en

IEEE: Copy

MOUSA REZAEE, and REZA JAHANGIRI, “NONLINEAR VIBRATIONS OF SANDWICH FG PLATES RESTING ON NONLINEAR PASTERNAK FOUNDATION UNDER PRIMARY RESONANCE EXCITATION USING MODIFIED FSDT,” MODARES MECHANICAL ENGINEERING, vol. 14, no. 15, pp. 186–198, 2015, [Online]. Available: https://sid.ir/paper/177683/en

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