GEOMETRICALLY NONLINEAR FREE VIBRATIONS OF FUNCTIONALLY GRADED BEAM WITH DISCONTINUITIES RESTING ON NONLINEAR ELASTIC FOUNDATIONS

Abstract eng:
This paper studies the geometrically nonlinear free vibration characteristics of functionally graded beam clamped at both ends with an edge crack and including uniform porosities resting on an elastic foundation. The theoretical formulations is based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity assumptions. A semi-analytical model based on Hamilton’s principle and spectral analysis combined with a homogenisation method is used to reduce the problem under consideration to that of an equivalent isotropic homogeneous cracked beam resting on an elastic foundation. A modified rule of mixture, taking the effect of porosities into account, is adopted in evaluating the effective material properties and assumed to be varying continuously in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The problem is solved by a numerical iterative method which investigates the effects of crack depth, material property gradient, foundations parameters, on dynamic response of cracked functionally graded beam.

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