Dynamical analysis of multilayered cantilevers

Abstract

A three-layered clamped-free (cantilevered) beam is considered and the nonlinear vibrations is investigated for the first time; internal resonances and complex vibrations are also investigated. Based on constitutive relations and Hamilton's principle, the kinetic and potential energies are constructed and balanced leading to nonlinear coupled equations for transverse and axial motions. Using inextensibility condition, a model of the cantilevered beam with inertial and stiffness nonlinearities is obtained. This is discretised using Galerkin's method and solved using a continuation method in the framework of pseudo-arclength. The nonlinear oscillation behaviour is analysed with special attention to the nonlinearities due to large-amplitude deflections. Different layer thickness and composition effects on the nonlinear oscillation are discussed. It is shown that when the system key parameters are selected carefully, a complex oscillation behaviour with internal resonance is displayed.