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The integral method and sensitivity analysis for strain modes of cantilever beam-like structures
Author(s): 
Pages: 855-864
Year: Issue:  6
Journal: Journal of Vibration Engineering

Keyword:  strain modecurvature modeintegral methodsensitivity analysiscurvature gradient mode;
Abstract: 应变模态振型决定了结构动应变分布规律.基于梁应变与曲率的正比关系,提出一种直接求解悬臂梁结构曲率模态的积分方法,适用于任意形式的刚度和质量函数.通过与数值和解析解比较模态频率与振型,验证了该方法的准确性.此外,该方法将连续体模态求解问题转化为有限自由度的广义特征值形式,进一步证明可以应用Nelson法求解该形式的特征灵敏度,获得了曲率模态振型对于结构设计参数的灵敏度显式表达.为了表现动应变变化,提出了曲率梯度模态的概念,其参数灵敏度可由曲率模态灵敏度获得.算例结果表明:该方法可以有效地优化结构参数、避免动应变集中.该方法同样也适用于固支-固支和固支简支这两种边界条件.
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