On the use of different perturbation techniques for the simulation of the statistical behaviour of plates in the mid-frequency range using an efficient Wave Based Method

For the analysis of the dynamical behaviour of mechanical structures the Finite Element Method (FEM) and the Statistical Energy Analysis (SEA) are most commonly used. However, the first approach is limited to applications in the low-frequency range due to its computational load and its deterministic character. The SEA has a much lower computational load but is only applicable at high frequencies due to its underlying assumptions. In-between the low- and high-frequency ranges there is a relatively wide mid-frequency-range, for which neither FEM nor SEA is applicable. Recently, the Wave Based Method (WBM) has been proposed for structural dynamic problems in the mid-frequency range. It is an indirect Trefftz-based technique in that it approximates the dynamic response variables by a function series expansion of exact solutions of the governing differential equation. Previous validations have shown its superior convergence and reduced calculation times as compared to the FEM. Although the method increases the attainable frequency range, it is still a deterministic technique. Non-determinism (variability and uncertainty), however, cannot be ignored in the mid-frequency range and should be accounted for in a sensible way. It has been shown previously that when there is enough non-determinism in the dynamic properties of a system, the response statistics become insensitive to the source of non-determinism. Based on this principle, this paper compares several ways to randomise the response of a structural system by introducing random point mass distributions, random inclusions or random boundary conditions using the WBM. The intrinsic efficiency of the WBM and its capacity to include non-determinism in an efficient way enables the method to tackle problems up to the high-frequency range. A numerical example validates the applicability of the proposed method. The mean response, the outer bounds of the ensemble and the calculation efficiency of the different approaches are compared and discussed.

Publication year:2012

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