Multi-level homotopy perturbation and projection techniques for the reanalysis of quadratic eigenvalue problems: The application of stability analysis

• Published in: Mechanical systems and signal processing Vol. 52-53; pp. 88 - 104
• Main Authors: Massa, F., Lallemand, B., Tison, T.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2015; Elsevier
• Subjects: Combined approximation; Computational efficiency; Damped asymmetric system; Dynamical systems; Eigenvalues; Engineering Sciences; Homotopy perturbation; Mathematical models; Mechanics; Parametric analysis; Perturbation methods; Projection; Projection technique; Reanalysis; Stability analysis; Homotopy perturbation; Reanalysis; Stability analysis; Damped asymmetric system; Combined approximation; Projection technique; "Reanalysis"; "Homotopy perturbation"; "Projection technique"; "Damped asymmetric system"; "Stability analysis"; "Combined approximation"
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2014.07.013

Complex eigenvalue analysis is widely used to investigate the stability of a dynamical system with frictional contact. For finite element models, iterative solvers are needed to precisely calculate complex modes and eigenvalues. However, in cases such as reanalysis studies, optimization or uncertainty propagation processes, computational cost can quickly become too time consuming. For multiple samplings, two methods combining homotopy perturbation and projection techniques are proposed for the reanalysis of quadratic eigenvalue problems. To highlight the efficiency of the proposed methods, a complete numerical application including nominal and perturbed solution calculations, coalescence graph and parametric analysis, is performed. The precision of results and computational time are compared with those obtained using commercial software. •Reanalysis of Quadratic Eigenvalue Problems for multiple samplings.•Coupling of homotopy perturbation and projection technique.•Calculation of eigensolutions perturbations with two-level homotopy techniques.•Reduction of computational time with regard to commercial software.