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.

中文翻译：

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基于可变粘弹性基础的耦合梁系统的自由和受迫振动

本文提出了一种改进的变分方法，用于对基于各种粘弹性基础的耦合梁系统进行自由和受迫振动分析。在耦合梁系统中考虑了非均匀以及均匀弯曲和直线 Timoshenko 梁组件。使用适当的坐标变换，通过结合拉格朗日乘子法和最小二乘加权残差法来适应耦合梁系统的梁组件之间的相互作用。同时制定了包括弹性边界条件在内的各种边界条件的界面势能。因此，所提出的方法允许灵活选择可接受的函数，而不管边界条件如何。基于所提出的能量方法，Winkler，Pasternak甚至以抛物线或正弦方式分布的可变基础可以很容易地引入到耦合梁系统中。两种阻尼，即比例阻尼和粘性阻尼，也被用来模拟粘弹性地基的能量耗散。在可能的情况下执行相应的有限元 (FE) 模拟并观察到良好的一致性。因此，对于耦合梁系统的自由、稳态和瞬态振动，证明了本方法的高效率和准确性。还研究了可变粘弹性基础参数对耦合梁系统动力特性的影响。也被用来模拟粘弹性地基的能量耗散。在可能的情况下执行相应的有限元 (FE) 模拟并观察到良好的一致性。因此，对于耦合梁系统的自由、稳态和瞬态振动，证明了本方法的高效率和准确性。还研究了可变粘弹性基础参数对耦合梁系统动力特性的影响。也被用来模拟粘弹性地基的能量耗散。在可能的情况下执行相应的有限元 (FE) 模拟并观察到良好的一致性。因此，对于耦合梁系统的自由、稳态和瞬态振动，证明了本方法的高效率和准确性。还研究了可变粘弹性基础参数对耦合梁系统动力特性的影响。