Forced Vibration Analysis of Euler-Bernoulli Double-Beam Systems by Means of Green’s Functions

Abstract

Double-curved-beam (DCB) systems are usually seen in many engineering fields. Compared to straight double-beam systems, DCB systems are more efficiency in noise and vibration control problems. This work aims to obtain closed-form solutions of steady-state forced vibrations of DCBs. The classical Euler-Bernoulli curved beam (ECB) model is employed in this work to modelling vibration equations of the DCB systems. The Green’s function and Laplace transform methods are successively used to obtain fundamental solutions for the vibration equations of the DCB systems. In this work, the fundamental solutions are general solutions and can be used for any boundary conditions. In numerical section, the present solutions are verified by comparing to some results in references. Effects of some important geometric and physical parameters on vibration responses and the interaction between the stiffness of the elastic layer and the DCB system are discussed. The results show that the DCB system can be degenerated to the straight double-beam system by setting two radiuses to infinity, and the DCB system also can be reduced to a double-beam system whose one upper or lower beam is a straight beam and the other is a curved beam.