In this paper, a modified variational method is developed to study the free and forced vibration of coupled straight–curved beam systems with an arbitrary number of eccentric discontinuities (EDs). Based on the generalized shell theory, the kinetic and potential functional of the curved beam with arbitrary subtended angles is formulated. Since the shear and inertial (or radial–tangential–rotational coupling) effects are included for the curved beam, the longitudinal vibration is also introduced to the energy functional for a straight Timoshenko beam. Using corresponding coordinate transformations, the Lagrange multiplier method and least-square weighted residual method are employed to impose the continuity constraints on the internal interfaces and boundaries among the straight and curved beams. The proposed method allows a flexible choice of the admissible functions and can be used for various combinations of the straight and curved beams to model corresponding engineering structures. Concentrated forces, uniformly distributed loads and space-dependent loads are considered to demonstrate great efficiency and accuracy of the present approach for the forced as well as the free vibration of the coupled system. Most of the present results are compared with those from finite element program ANSYS, and good agreement is observed. Influences of the EDs on the dynamic responses of the coupled system are also examined.

中文翻译：

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承受各种谐波力的具有任意间断的耦合直线弯曲梁系统的振动分析

在本文中，开发了一种改进的变分方法来研究具有任意数量的偏心不连续点（ED）的耦合直弯曲梁系统的自由振动和强迫振动。基于广义壳理论，提出了任意对角弯梁的动力学和势函数。由于弯曲梁包括剪切和惯性（或径向-切向-旋转耦合）效应，因此纵向振动也被引入到直线型Timoshenko梁的能量函数中。通过相应的坐标变换，采用拉格朗日乘数法和最小二乘加权残差法将连续性约束强加给直光束和弯光束的内部界面和边界。所提出的方法允许灵活选择允许的功能，并且可以用于直梁和弯曲梁的各种组合以对相应的工程结构建模。考虑集中力，均匀分布的载荷和与空间有关的载荷，以证明本方法对于耦合系统的强迫振动和自由振动具有很高的效率和准确性。目前的大多数结果与有限元程序ANSYS的结果进行了比较，并观察到了很好的一致性。还检查了ED对耦合系统动态响应的影响。考虑均匀分布的载荷和与空间有关的载荷，以证明本方法对于耦合系统的强迫振动和自由振动具有很高的效率和准确性。目前的大多数结果与有限元程序ANSYS的结果进行了比较，并观察到了很好的一致性。还检查了ED对耦合系统动态响应的影响。考虑均匀分布的载荷和与空间有关的载荷，以证明本方法对于耦合系统的强迫振动和自由振动具有很高的效率和准确性。目前的大多数结果与有限元程序ANSYS的结果进行了比较，并观察到了很好的一致性。还检查了ED对耦合系统动态响应的影响。