Effect of Boundary Conditions and Taper Patterns on Geometrically Nonlinear Frequency Response of Axially Graded Beams on Elastic Foundation

Abstract

Forced vibration analysis is performed on a tapered axially functionally graded beam resting on elastic foundation under externally applied harmonic excitations to present the effect of boundary conditions and taper patterns on the frequency response. The elastic foundation is modelled in the present analysis as Winkler foundation. A displacement based semi-analytical method is adopted for mathematical formulation and the derivation of governing equations is carried out following Hamilton s principle. Von Karman nonlinear strain-displacement relation employed to incorporate geometric nonlinearity. Broyden method is adopted to solve the nonlinear set of equations. Frequency response curves are plotted in non-dimensional frequency-amplitude plane to represent nonlinear forced vibration characteristic of the system. New benchmark results are also provided for different combination of system parameters (i.e., excitation amplitudes, foundation stiffness values, material models, taper patterns, and flexural boundary conditions). Operational deflection shapes (ODS) are also presented.