A closed-form analytical solution method for vibration analysis of elastically connected double-beam systems

摘要

A double-beam system, which is a structure composed of two parallel beams that are interconnected by a viscoelastic layer, is seen in many engineering applications. Vibration analysis is essentially important for the safe and reliable operation, and optimal design of such dynamic systems. This paper presents an analytical method, the distributed transfer function method (DTFM), for modeling and vibration analysis of double-beam systems with arbitrary beam linear densities and flexural rigidities, and general boundary conditions. Exact closed-form analytical solutions for natural frequencies, mode shapes, and steady-state responses to periodic excitations are determined. The proposed method is applicable to a double-beam system with lower beam being fully, partially, or not supported by an elastic foundation. Through numerical study, the accuracy and efficiency of the proposed method are validated, and the effects of the stiffness, length, and location of an elastic foundation are investigated. It is shown that the DTFM is a useful tool for optimal design of elastically connected double-beam systems.