Homotopy perturbation technique for improving solutions of large quadratic eigenvalue problems: Application to friction-induced vibration

• Published in: Mechanical systems and signal processing Vol. 153; p. 107492
• Main Authors: Sadet, Jérémy, Massa, Franck, Tison, Thierry, Turpin, Isabelle, Lallemand, Bertrand, Talbi, El-Ghazali
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15.05.2021; Elsevier BV; Elsevier
• Subjects: Damping; Eigenvalues; Engineering Sciences; Finite element method; Frequencies; Friction-induced vibration; Homotopy; Mathematics; Mechanics; Nonlinear vibration; Perturbation; Perturbation methods; Projection; Quadratic Eigenvalue Problem; Stiffness matrix; Vibration; Vibrations; Projection; Perturbation; Quadratic Eigenvalue Problem; Homotopy; Nonlinear vibration; Friction-induced vibration
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2020.107492

•Generalization of the classical projection basis for solving a QEP.•Improvement of projection basis with high order perturbed modes.•Stabilization of complex eigensolutions in the entire frequency band of interest.•Increase of results confidence by QEP residue reduction. This paper puts forward a projection technique for accurately calculating solutions of large Quadratic Eigenvalue Problem. The aim here is to stabilize the complex eigensolutions whilst reducing residual errors, especially when considering significant damping contribution or asymmetric stiffness matrices. Hence, more confident results can be obtained in the frequency band of interest. To achieve this, high order modes, calculated using the homotopy perturbation technique, are introduced in the projection step of the classical method. This numerical proposal is a generalization of the classical projection, based only on normal modes of the associated undamped problem. To evaluate the efficiency of the suggested method, a finite element application dedicated to a friction-induced vibration problem is investigated.