Non-linear forced vibration analysis of axially functionally graded tapered beam with various end conditions

Abstract

In the present thesis a study of large amplitude forced vibration of axially functionally graded beams is carried out by considering various boundary conditions and loading condition. The governing differential equation for the system is derived by using Hamilton’s principle and the solution to the nonlinear set of equations is generated by implementing a substitution technique. The results of the nonlinear analysis are plotted as characteristics curve i.e. non-dimensional frequency response curve for different classical flexural boundary conditions with different variation of material and geometric parameters. For each boundary condition, variation of material properties (i.e. elastic modulus & density) in the axial direction of the beam is considered with different taper profile of thickness. The variation of material properties taken under consideration are homogenous material, linear variation of both elasticity and density, exponential variation both elasticity and density, linear variation of elasticity with quadratic variation of density. Four different taper profiles are taken into account, namely, uniform, linear, exponential, and parabolic, for thickness variation, while the width of the beam is kept constant.