Determination of natural frequency and amplitude ratio 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 effect of compressive axial load with a Keer layer in-between are studied in this paper. It is assumed that the two beams of the system are continuously joined by a Keer layer. The equations of 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 Kerr model, the most common methods used are 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 and associated amplitude ratio) of the considered model by applying the Rayleigh theory. 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.