The analysis of free vibration of conservative oscillators with inertia and static type cubic non-linearities by variational-Padé technique

Abstract

In this study, a new method based on the variational iteration method and the Pade approximation is introduced to obtain accurate analytical solutions for some special types of non-linear differential equations, arising in modelling the dynamic behaviour of oscillators with inertia together with cubic stiffness non-linearities. The comparison of the results of a new proposed variational Pade technique for analysing large-amplitude free vibrations of cantilever beams carrying a lumped mass and rotary inertia, with those of other conventional methods, ensures the excellent accuracy of the proposed method.