Free transverse vibration analysis of a Rayleigh double-beam system with a Keer middle layer subjected to compressive axial load

Abstract

Free transverse vibration of a Rayleigh double-beam system with the effect of compressive axial load with a Keer layer in-between is studied in this paper. It is assumed that the two beams of the system are continuously joined by the Keer layer. The equations of the motion for this system are described by a set of three homogenous differential equations. The classic Bernoulli-Fourier method was used for solving this system of differential equations. In the research found in literature on the subject of the Keer model, the most common methods used are the theories of Timoshenko and Euler-Bernoulli. It is for that exact reason that the research goal of this paper is determining analytical and numerical characteristics (natural frequency, associated amplitude ratio) of the considered model by applying the Rayleigh theory. What is also researched is the effect of elastic in-between layer on system's frequency and amplitudes. The numerical analysis of the system was performed using software tools. The numerical results obtained are shown in the form of a plot diagram. Presented numerical results in this paper confirm those obtained in the literature.