Large amplitude forced vibration analysis of an axially functionally graded tapered beam resting on elastic foundation

Abstract

A displacement based semi-analytical method is utilized to study large amplitude forced vibration of a linearly tapered axially functionally graded (AFG) beam resting on an elastic foundation. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. The external excitation is assumed as harmonic and the system response is considered to have the same frequency as that of the external excitation. The frequency of excitation and the maximum amplitude of the harmonic excitation are supplied and the corresponding unknown coefficients are determined. At the peak load value it is assumed that the system satisfies the force equilibrium condition. Thus the dynamic problem is solved as a static one through an iterative scheme using a relaxation parameter. Energy principles are used for the formulation of the problems. The free vibrational frequencies are tabulated for various boundary conditions and foundation stiffness. The dynamic behavior of the system is presented in the form frequency response curve.