Nonlinear Free Vibration Analysis of Tapered Hollow Beam

Abstract

Nonlinear free vibration analysis is carried out on tapered hollow beam for different types of flexural boundary conditions. Mathematical modelling is formulated by using the variational form of energy principles. Due to large deflection of the tapered hollow beam geometric nonlinearity comes into picture. To account for the nonlinearity in the system, nonlinear strain displacement relations are considered. The Free vibration analysis of hollow beam is carried out in two parts. In first part static analysis, which is based on the principle of minimum total potential energy, is solved for the unknown static displacement field. In second part dynamic analysis, which is based on Hamilton’s principle, is performed, based on the result, obtained from the static analysis. Load-deflection plots and backbone curves are presented for the tapered hollow beam. Also comparative plots between hollow and solid beams have been shown. The results are validated with those available in the literature.