Dynamics of axially functionally graded nonuniform beam with geometric nonlinearity

Abstract

In this article, the nonlinear dynamic behavior of axially functionally graded non-uniform beam is investigated using finite element method. The beam material is graded in the axial direction following the exponential rule and three different taper profiles are selected namely; linear, parabolic and exponential. Euler-Bernoulli beam theory is utilized along with Hamilton’s principle to formulate the forced vibration problem. Geometric nonlinearity present in the system is taken care of using von Karman type nonlinear geometrical relations. The beam is considered to be under the action of uniformly distributed external excitation of harmonic nature. The results are validated with those available in the literature and new results are presented showing the effect of material gradient parameter, excitation amplitude, taper profile and taper parameter on the frequency response curves.