Finite Element Based Static and Dynamic Vibration Analysis of a Beam with Axial Variation of Material Properties

Abstract

The study examines the vibration analysis of a damped cantilever beam with nonuniform variation in material properties using finite element methods. With power modification of material parameters in the axial direction, the static and dynamic response of a prismatic rectangular beam with damping has been examined. For the finite element approach, two noded beam elements with two degrees of freedom at each node were evaluated. The power law variation of material properties was used throughout the investigation. This research investigated the effects of proportional damping on displacement, velocity, and acceleration responses. The proposed beam's mass, stiffness, and damping matrices were calculated using Hamilton's concept. In the temporal domain, the Newmark Method has been utilized