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广义微分求积法与分析法在分析非均匀纳米梁系统的振动行为中的对比

Hessam Bakhshi Khaniki1, Shahrokh Hosseini Hashemi2, Hossein Bakhshi Khaniki2
1、谢里夫理工大学工业工程系，德黑兰，伊朗
2、伊朗科技大学机械工程学院，德黑兰，伊朗

摘要


这篇文章采用广义微分求积法（GDQM）研究可变截面纳米梁的自由振动行为。采用 Eringen 的非局部弹性理论模拟小尺度效应，并通过指数化改变纳米梁的宽度来假设非均匀性。选取不同数量的采样点，采用广义微分求积法解决运动控制方程。对前三个频率参数增加采样点可以得到更准确的结果，并且选取特定的采样点数量后，结果会合并为一定精确的数字。结论是，与分析结果相比，采用广义微分求积法能够得到正确的答案。此外，由于小尺度结构的刚度软化行为，使用 Eringen 的非局部弹性理论来模拟频率变化引起的小尺度效应是必要的。

关键词


广义微分求积法；GDQM；纳米梁；非局部梁；非均匀梁；可变截面



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