Abstract
In the present paper, the responses of nonlinear functionally graded beams (FGBs) under harmonic and random excitation are studied based on the averaging method for strongly nonlinear systems. Due to the asymmetry of the functionally graded materials (FGMs), the neutral layer will shift from the geometric center plane. The position of the neutral layer is determined according to the varying properties of the FGMs and the equilibrium equation. First, the effects of the material gradient index on the position of the neutral layer are analyzed. Then, the nonlinear vibration equation of FGBs under external excitation is established. The nonlinear dynamical equations of the generalized coordinates are obtained by using the Galerkin discretization. The averaging method for strongly nonlinear systems under deterministic and random excitation is developed to derive the approximate analytical responses. The effects of functional gradient index, excitation frequency, noise intensity and other parameters on the dynamical response are investigated. The effectiveness of the proposed analytical method is verified by the numerical simulation.
Published Version
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