Analysis of parametric instability of a spring-attached pre-twisted beam with viscoelastic end support

Abstract

This study investigated the parametric instability of a single elastic beam with spring attachment on the top and viscoelastic springs as end supports. The beam considered is pre-twisted with a pin connection at both ends that supports the beam. The analytical solution of the problem is expressed in the matrix form achieved from the implementation of Hamilton’s principle and General Galerkin’s method, from which both static and dynamic stability of the beam can be investigated. The results of various influential dimensionless parameters such as stiffness, mass, length, position of the spring attachment, and stiffness of the viscoelastic springs on both the stabilities are studied. This analysis concluded that the spring attachment on the system leads to substantial contribution in improving the stability. The viscoelastic springs also contribute in upsurging the beam’s stability. Three different profiles of the beam have been considered, and for each profile, three different types of springs have been examined. The results revealed that the beam with parabolic profile and stiffness of the spring attachment with parabolic variation is most effective towards strength-to-weight ratio.