In this article, flexural vibration and its power flow of an axially loaded beam with arbitrary boundary and non-uniform elastic foundation are analyzed via energy principle in conjunction with Rayleigh–Ritz procedure. A general solution is assumed as a modified version of Fourier series supplemented with boundary-smoothing auxiliary terms. Effects of axial load and elastic foundation of the beam are taken into account in terms of potential energy in system Lagrangian. Critical load of this axially loaded beam is obtained under elastic boundary condition and non-uniform foundation. Numerical examples are then presented to demonstrate the reliability and effectiveness of the established model by comparing results with those available in literature or calculated using finite element method. Results show that the current model can make an accurate dynamic analysis for the elastically restrained beam with axial load and non-uniform elastic foundation. Influence of some important factors, including boundary restraint, axial load, and non-uniform foundation, on the vibration characteristics and power flow transmission are studied and addressed. It is found that the supporting condition has a significant influence on power flow distribution across the whole beam, in which the shear force component plays a dominant role for the power flow transmission.

在本文中，通过能量原理结合瑞利-里兹程序，分析了具有任意边界和不均匀弹性基础的轴向荷载梁的弯曲振动及其功率流。假定一般解决方案为傅立叶级数的改进版本，并辅以平滑边界的辅助项。考虑了拉格朗日系统中的势能，考虑了梁的轴向载荷和弹性基础的影响。该轴向加载梁的临界载荷是在弹性边界条件和不均匀基础下获得的。然后通过数值例子来证明所建立模型的可靠性和有效性，方法是将结果与文献中的结果进行比较或使用有限元方法进行计算。结果表明，该模型可以对具有轴向载荷和弹性地基不均匀的弹性约束梁进行精确的动力分析。研究并解决了边界约束，轴向载荷和基础不均匀等重要因素对振动特性和动力传递的影响。发现支撑条件对整个梁上的潮流分布有重要影响，其中剪切力分量在潮流传递中起主要作用。研究了振动特性和动力传递问题。发现支撑条件对整个梁上的潮流分布有重要影响，其中剪切力分量在潮流传递中起主要作用。研究了振动特性和动力传递问题。发现支撑条件对整个梁上的潮流分布有重要影响，其中剪切力分量在潮流传递中起主要作用。