Free and forced vibration of double beam with arbitrary end conditions connected with a viscoelastic layer and discrete points

Abstract

The Double-Beam System with Intermediate Supports composed of two parallel beams, arbitrary intermediate supports, and an optional interconnecting viscoElastic Layer (DBS-ISEL) has many engineering applications. However, few publications have developed the exact and explicit mode shape solutions of free vibrations of the DBS-ISEL by far, and the forced vibrations of the DBS-ISEL are not systematically treated. In this work, the free and forced vibrations of the general configuration of the DBS-ISEL under the general boundary conditions are systematically attacked. An analytical solution in closed-form is formulated based on the orthogonality conditions of the mode shape solutions. A general numerical solution is also presented. Numerical examples are demonstrated to show that the proposed solution agrees well with the literature. For the damped vibrations, the asymptotic deflections of the two beams converge to the static deflections. The parametric study shows that the intermediate elastic support could effectively modulate the deflections of the beams. This research is beneficial to the designing, monitoring and maintaining of the DBS-ISEL.