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On the modal decoupling of linear mechanical systems with frequency-dependent viscoelastic behavior

机译：具有频率依赖的粘弹性行为的线性机械系统的模态解耦

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摘要

Linear Multi-Degree of Freedom (MDOF) mechanical systems having frequency-dependent viscoelastic behaviors are often studied and modelled in frequency or Laplace domains. Indeed, once this modelling process is carried out, it is not generally possible to reduce the obtained MDOF damped mechanical system to a set of uncoupled damped modal oscillators apart from some special cases. In this paper a general procedure has been proposed to transform a coupled linear mechanical system having frequency-dependent viscoelastic characteristics to a set of independent damped modal oscillators. The procedure is based on a linear co-ordinate transformation procedure using matrices in real field only. The approach is exact and based on the solution of one associated eigen-problem for the case of linearly viscous damping. In the general case of frequency-dependent viscoelastic materials, the approach includes an iterative procedure solving local eigenproblems.Some numerical results are reported to show the capabilities of the proposed approach.
机译：具有频率依赖性粘弹性行为的线性多自由度（MDOF）机械系统通常在频域或拉普拉斯域中进行研究和建模。实际上，一旦执行了该建模过程，除了某些特殊情况外，通常不可能将获得的MDOF阻尼机械系统简化为一组未耦合的阻尼模态振荡器。在本文中，已经提出了将具有依赖于频率的粘弹性特性的耦合线性机械系统转换为一组独立的阻尼模态振荡器的通用程序。该过程基于仅使用实场中的矩阵的线性坐标变换过程。该方法是精确的，并且基于线性粘滞阻尼情况下一个相关的本征问题的解。在频率依赖的粘弹性材料的一般情况下，该方法包括求解局部特征问题的迭代程序。据报道，一些数值结果表明了该方法的功能。

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