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A multiscale 'Trefftz' computational method for medium-frequency vibrations of assemblies of heterogeneous plates with uncertainties

机译:具有不确定性的非均质板组件中频振动的多尺度“ Trefftz”计算方法

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摘要

A new approach, called the "Variational Theory of Complex Rays", is being developed for the calculation of the vibrations of slightly damped elastic plates in the medium-frequency range. In this approach, the resolution of a small system of equations which does not result from a refined spatial discretization of the structure leads to the evaluation of effective quantities (deformation energy, vibration amplitude,...). This theory has already been validated for assemblies of homogeneous substructures and extended to the case of heterogeneous substructures. In this paper, we propose some improvements to deal with sensitivity analysis. The objective is to evaluate the influence of discontinuities with uncertain positions, sizes or directions on the structural response. A specific partial inversion of the constrained system of equations enables multiple resolutions for combinations of the parameters defining the possible shapes of the discontinuity to be carried out at low cost.
机译:正在开发一种新的方法,称为“复杂射线的变化理论”,用于计算中频范围内略微阻尼的弹性板的振动。在这种方法中,不是由精细的结构空间离散化导致的方程式小系统的分辨率导致对有效量(变形能量,振动幅度等)的评估。该理论已被均质子结构的装配所验证,并扩展到异质子结构的情况。在本文中,我们提出了一些改进来处理敏感性分析。目的是评估位置,大小或方向不确定的不连续点对结构响应的影响。约束方程组的特定局部反转使得能够以低成本实现用于定义不连续性的可能形状的参数组合的多种分辨率。

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