轴向力作用任意不连续梁自由振动分析的广义函数解

摘要：首先运用分布理论建立了轴向力作用下含多个不连续点的欧拉梁的自由振动的统一微分方程。不连续点的影响由广义函数（Dirac delta函数）引入梁的振动方程。微分方程运用Laplace变换方法求解；与传统方法不同的是，本文方法适用于含任意类型的不连续点和多种不连续点组合情况的梁，求得的模态函数为整个不连续梁的一般解。由于模态函数的统一化以及连续条件的退化，特征值的求解得到了极大的简化。最后，以轴向力作用下多跨梁—弹簧质量块系统模型为例验证了本文方法的正确性与有效性。

Free vibration analysis of discontinuous beams under axial force using generalized functions

Abstract：The general governing differential equation of the vibration of Euler-Bernoulli beams with multiple discontinuities subjected to axial force presented by using generalized functions. The equation is then solved based on Laplace transformation. Unlike the classical solutions of discontinuous beams, the proposed scheme is valid in arbitrary miscellaneous discontinuities conditions, the generalized solutions are expressed in the terms of a single expression on the entire beam. As the specified discontinuities type, eigenvalue matrices are simplified by the degenerated continuity conditions. Final, the accuracy and efficiency of the proposed method is verified with an example of the free vibration problems for a four-span simply supported beam with three spring-mass systems subject to compressive force.Final, the free vibration problems for (a) a beam with masses and their rotatory inertias, (b) a four-span pinned-pinned beam with three spring-mass systems subject to compressive force, (c) a multiple cracked beam with axial force and elastic foundation are studied. It is shown that the present method offers an accurate and effective method of free vibration analysis of beams with arbitrary discontinuities.