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Nonintrusive parametric solutions in structural dynamics
Computer Methods in Applied Mechanics and Engineering, Volume: 389, Start page: 114336
Swansea University Author: Rubén Sevilla
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A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-dened parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corr...
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A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-dened parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corresponding mode shapes.A parametric version of the inverse power method (IPM) is presented by using the proper generalised decomposition (PGD) rationale. The proposed approach utilises the so-called encapsulated PGD toolbox and includes a new algorithm for computing the square root of a parametric object. With only one offline computation, the proposed PGD-IPM approach provides an analytical parametric expression of the smallest (in magnitude) eigenvalue (or natural frequency) and corresponding eigenvector (mode shape), which contains all the possible solutions for every combination of the parameters within pre-dened ranges. A Lagrange multiplier deation technique is introduced in order to compute subsequent eigenpairs, which is also valid to overcome the stiff-ness matrix singularity in the case of a free-free structure. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial nite element (FE) packages. Two numerical examples are shown to underline the properties of the technique. The rst example includes one material and one geometricparameter. The second example shows a more realistic industrial example, where the nonintrusivity of the approach is demonstrated by employing a commercial FE package for assembling the FE matrices. Finally, a multi-objective optimisation study is performed proving that the developed method could signicantly assist the decision-making during the preliminary phase of a new design process.
Algebraic PGD; Parametric Modal Analysis; Reduced Order Model; Shape Optimisation
Faculty of Science and Engineering
This project is part of the Marie Skłodowska-Curie ITN-EJD ProTechTion funded by the European Union Horizon 2020 research and innovation program with Grant Number 764636. The work of Fabiola Cavaliere, Sergio Zlotnik and Pedro D´ıez is partially supported by the MCIN/AEI/10.13039/501100011033, Spain (Grant Number: PID2020-113463RB-C32, PID2020-113463RB-C33 and CEX2018-000797-S). Ruben Sevilla also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant Number: EP/P033997/1).