A power series solution for rotating nonuniform Euler-Bernoulli cantilever beams
A power series solution for rotating nonuniform Euler-Bernoulli cantilever beams
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DOI：
10.1177/1077546317714183
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发表时间：
2018-09-01
影响因子：
2.8
通讯作者：
Jaeger, Martin
中科院分区：
文献类型：
--
作者：
Adair, Desmond;Jaeger, Martin
本文建立了一个系统的方法来研究根部受弹性约束的旋转变截面欧拉-伯努利梁的动力响应。为了找到解决方案，一种新的方法是使用在描述振动问题的四阶微分方程首先被写为一阶矩阵微分方程，然后使用幂级数法求解。该方法可用于非均匀Euler-Bernoulli梁振动问题的近似解。具体而言，数值例子在这里展示的有用性的非均匀欧拉-伯努利固定自由悬臂梁的频率分析的方法。模态振型和频率参数的结果被认为是在令人满意的协议与以前发表的结果。锥形的影响，平等和不平等，悬臂楔和悬臂锥进行了研究。
A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler-Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler-Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler-Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.