Nonlinear Forced Vibrations of Thin Circular and Elliptical Functionally Graded Plates

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Ghaheri, Ali | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46659 (08)
University: Sharif University Technology
Department: Mechanical Engineering
Advisor(s): Nosier, Asghar
Abstract:
Nonlinear forced vibrations of thin functionally graded circular and elliptical plates under classical boundary conditions are investigated based on the classical plate theory. The von Kármán strain-displacement relations is employed to include geometrical nonlinearity caused by large transverse displacements of the plate thickness order, and modal expansion in polar and elliptical coordinate along with the perturbation method of multiple scale is used to solve the governing equations. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. Transverse forcing is supposed to be harmonic with angular frequency near to the natural frequencies of plate. Nonlinear vibration phenomena such as jump phenomenon and internal resonance are studied and the effects of boundary conditions, power-law distribution, amplitude and frequency of external pressure on dynamical behavior are examined. The validity of results is established by comparison with the existing results in the literature as well as FEM results
Keywords:
Analytical Solution ; Perturbation Method ; Functionally Graded Materials (FGM) ; Von Karman Theory ; Circular Plate ; Nonlinear Vibration ; Elliptical Plate

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