Free and Forced Vibration of Coupled Beam Systems Resting on Variable Viscoelastic Foundations

Abstract

This paper presents a modified variational method for free and forced vibration analysis of coupled beam systems resting on various viscoelastic foundations. Non-uniform as well as uniform curved and straight Timoshenko beam components are considered in the coupled beam system. Using proper coordinate transformations, interactions among the beam components of the coupled beam system are accommodated by combining Lagrange multiplier method and least-square weighted residual method. Interface potential energy for various boundary conditions including the elastic ones is simultaneously formulated. Thus, the proposed method allows flexible choice of the admissible functions, regardless of the boundary conditions. Based on the proposed energy method, Winkler, Pasternak or even variable foundations distributed in a parabolic or sinusoidal manner can be easily introduced into the coupled beam systems. Two kinds of damping, namely the proportional and viscous damping, are also employed to model the energy dissipation of the viscoelastic foundations. Corresponding finite element (FE) simulations are performed where possible and good agreement is observed. Thus, great efficiency and accuracy of the present approach are demonstrated for free, steady-state and transient vibration of the coupled beam systems. The influences of the parameters of the variable viscoelastic foundations on the dynamic properties of the coupled beam system are also examined.