On the dynamic response of beams with multiple geometric or material discontinuities
On the dynamic response of beams with multiple geometric or material discontinuities
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DOI：
10.1016/j.ymssp.2009.11.009
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发表时间：
2010-07
影响因子：
8.4
通讯作者：
S. Stanton;B. Mann
中科院分区：
文献类型：
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作者：
S. Stanton;B. Mann
为确定具有任意数量几何或材料不连续的欧拉-伯努利梁的固有频率、模态振型和频率响应函数的封闭形式表达式，开发了一个解析框架。该程序采用一种方便的矩阵公式将单不连续梁问题推广到具有多阶跃变化的梁。具体地说，通过将总结构分析为一系列不同的欧拉-伯努利单元，并在分离位置强制连续性和相容性来解决多重不连续梁问题。该方法产生每个各自部分的特征模态，然后可以将其叠加以给出整个梁的模态形状，并推导出频率响应函数。虽然证明了欧拉-伯努利梁问题，但任何一维连续结构都适用于规定的分析。理论预测也得到了实验验证。
An analytic framework is developed for determining closed form expressions for the natural frequencies, mode shapes, and frequency response function for Euler–Bernoulli beams with any number of geometric or material discontinuities. The procedure uses a convenient matrix formulation to generalize the single discontinuity beam problem to beams with multiple step changes. Specifically, the multiple discontinuity beam problem is solved by analyzing the total structure as a series of distinct Euler–Bernoulli elements with continuity and compatibility enforced at separation locations. The method yields each respective section's eigenmode which may then be superpositioned to give the entire beam's mode shape and derivation of the frequency response function follows. Although the Euler–Bernoulli beam problem is demonstrated, any one-dimensional continuous structure is amenable to the prescribed analysis. Theoretical predictions are experimentally validated as well.