The flexural vibration and buckling of the elastically connected parallel-beams with a Kerr-type layer in between

Abstract

This paper presents an analytical theory to define the dynamic characteristics of the elastically connected parallel-beams under compressive axial loading. It is assumed that the two parallel-beams of the system are simply supported and continuously joined by a Kerr-type three parameter model. The motion of the system is described by a set of three homogeneous partial differential equations, which are solved by using the classical Bernoulli-Fourier method. The natural frequencies, associated amplitude ratio and the critical buckling load for complex system are determined. The presented theoretical analysis is illustrated by a numerical example and results compared with the results in papers Oniszczuk (2000) and Zhang et al. (2008). © 2013 Elsevier Ltd.