Uncertainty Quantification in Structures

Date(s)
Thursday 30th January 2025 (15:00-16:00)
Contact
Event Convenor Contact: Martin.Richter@nottingham.ac.uk
Description
Speaker's Name: Michael Nieves
Speaker's Affiliation: University of Keele
Speaker's Research Theme(s): Applied Mathematics,Wave modelling
Abstract:
We discuss an asymptotic approach used to accurately predict the vibration response of elastic solids containing clusters of defects. We consider 2D composites [1], where defect clusters are represented by closely interacting small inclusions of different sizes, geometries and physical properties. The approach is based on the so-called method of mesoscale approximations, previously developed for quasi-static problems [2]. The resulting approximations make use of model solutions to dynamic problems (i) posed in the medium when the defects are absent and (ii) involving individual defects. These model solutions are combined with appropriate weights that solve a linear algebraic system, which naturally appears in attempting to satisfy the boundary conditions for the solid to a high order of accuracy. This system contains information about the geometrical properties of each defect, as well as their interaction. The method presented yields uniformly accurate approximations for fields associated with scattering problems and eigenmodes of finite solids containing defect clusters. It also allows one to obtain effective models for the cluster at low frequencies. The theoretical results are accompanied by numerical illustrations that demonstrate the effectiveness of the approach. References: [1] Nieves, M.J. and Movchan, A.B. (2022). Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions. Phil. Trans. R. Soc. A.380: 20210392. http://doi.org/10.1098/rsta.2021.0392 [2] Maz'ya V.G., Movchan, A.B., Nieves, M.J. (2013): Green's Kernels and Meso-Scale Approximations in Perforated Domains, Lecture Notes in Mathematics, pp. XVII, 258, Springer Cham. https://doi.org/10.1007/978-3-319-00357-3
Keywords: asymptotics, vibrations, mesoscale, eigenvalues
Venue: UP-Psychology B37

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