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Free vibration and physical parameter identification of non-uniform composite beams

机译：非均匀组合梁的自由振动和物理参数识别

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摘要

A new low order analytical model is developed for the analysis of non-uniform composite beams, which approximates the dynamic behavior of the continuous system accurately and solves the associated direct and inverse problems. The analysis of some non-uniform composite beams is considered that are governed by Bernoulli-Euler beam equations. The mathematical model approximates the non-uniform composite beam, with another beam having piecewise constant material properties, leading to certain direct and inverse transcendental eigenvalue problems with transcendental matrix elements. Numerical methods are developed to solve such eigenvalue problems and several examples are solved. In solving direct problems, it is shown that the spectrum of non-uniform composite beams can be obtained with fair accuracy. Furthermore, it is also demonstrated that the physical parameters of piecewise composite beams can be reconstructed accurately from the spectral data obtained from vibration modal analysis experiments.
机译：建立了一种新的用于分析非均匀组合梁的低阶分析模型，该模型可以精确地逼近连续系统的动态行为，并解决相关的正反问题。认为对某些非均匀组合梁的分析受Bernoulli-Euler束方程的控制。数学模型近似非均匀复合梁，而另一束具有分段恒定的材料特性，从而导致先验矩阵元素具有某些直接和反先验特征值问题。开发了数值方法来解决这种特征值问题，并解决了几个例子。在解决直接问题时，显示出可以以相当高的精度获得非均匀复合梁的光谱。此外，还表明，可以根据从振动模态分析实验获得的光谱数据准确地重建分段组合梁的物理参数。

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