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A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

机译:分层分层梁的自由振动分析动态刚度元件

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摘要

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.
机译:开发了一种用于分层多层梁的弯曲振动分析的动态刚度元件,随后用于研究双层梁配置的自然频率和模式。利用Euler-Bernoulli弯曲光束理论,基于这些方程式的闭合形式解决方案,选择了管理微分方程和代表性,频率相关的场变量。然后施加边界条件以配制动态刚度矩阵(DSM),其涉及谐振载荷,以沿梁的谐振变化的位移。研究了一种说明性示例问题的弯曲振动,其特征在于可变长度的分层区域。还开发了两种基于传统有限元方法(FEM)和文献中报告的分析解决方案的计算机代码,并用于比较。从所提出的DSM方法获得的完整和有缺陷的光束自然频率和模式以及有限元和分析结果以及文献中的那些。

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