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

• Elastically connected parallel beams under compressive axial loading.
• Kerr type elastic layer.
• Explicit expressions of natural frequencies and the associated amplitude ratio.
• Effects of compressive axial load on the responses of the double beam system.

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).