Free vibration analysis of Euler-Bernoulli beams under non-classical boundary conditions
Free vibration analysis of Euler-Bernoulli beams under non-classical boundary conditions
复制标题
非经典边界条件下欧拉-伯努利梁的自由振动分析
DOI：
10.20906/cps/con-2016-1053
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发表时间：
2016
影响因子：
--
通讯作者：
S. Hoefel
中科院分区：
文献类型：
--
作者：
João Fernandes da Silva;Lucas Allende Dias do Nascimento;S. Hoefel
工程结构中经常会出现带有附件的柔性梁和非经典边界条件，对这类结构进行模态分析是结构设计中的重要内容。在各种实际情况下，对两端有弹性约束，不能转动和平移，或两端有集中质量或转动惯量的振动梁的分析是很有意义的。在分析中，首先建立梁的控制微分方程（变系数偏微分方程）和质量弹簧系统的控制微分方程（常微分方程），然后利用经典和非经典边界条件求出问题的精确解，并求出特征值和特征函数。并对文献中已有结果的一些实例进行了分析。
: The flexible beams carrying attachments and non-classical boundary conditions often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. The analysis of vibrating beams with ends elastically restrained against rotation and translation or with ends carrying concentrated masses or rotational inertias is of great interest in a variety of practical cases. In this analysis, the governing differential equations of the beam, which is a partial differential equation with variable coefficients, and that of the mass-spring system, which is an ordinary differential equation, are found. The exact solution of the problem is then obtained using classical and non-classical boundary conditions and the eigenvalues and eigenfunctions are found. Finally, some cases with available results in the literature are presented and analyzed.