Geometrically Non-Linear Free and Forced Vibration of Clamped-Clamped Functionally Graded Beam with Discontinuities.

摘要

This paper investigates the free and forced nonlinear vibration characteristics of functionally graded beam clamped at both ends with an edge crack and including uniform porosities. A modified rule of mixture, taking the effect of porosities into account, is adopted in evaluating the effective material properties and assumed to be graded in the thickness direction. 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. The problem is solved by a numerical iterative and explicit method. A detailed numerical study is conducted to examine the effects of crack depth, porosity, material property and the excitation frequency of the applied harmonic force on the dynamic behaviour of the cracked FGM beam.