On Harmonic Balance Method-based Lagrangian contact formulations for vibro-impact problems

• Published in: Journal of sound and vibration Vol. 531; p. 116950
• Main Authors: Vadcard, Thibaut, Batailly, Alain, Thouverez, Fabrice
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 04.08.2022; Elsevier Science Ltd; Elsevier
• Subjects: Asymptotic methods; Barriers; Comparative analysis; Constraint modelling; Engineering Sciences; Equivalence; Frequency response; Harmonic analysis; Harmonic balance method; Harmonics; Lagrange multiplier; Linear complementarity problem; Mechanical engineering; Mechanical systems; Mechanics; Nonlinear response; Nonsmooth dynamics; Oversampling; Physics; Stiffness; Time integration; Time signals; Unilateral contact; Vibrations; Unilateral contact; Nonsmooth dynamics; Linear complementarity problem; Harmonic balance method; méthode de l'équilibrage harmonique; mécanique non-régulière; contact unilatéral
• ISSN: 0022-460X; 1095-8568; 1095-8568
• DOI: 10.1016/j.jsv.2022.116950

This article assesses two Harmonic Balance Method-based numerical Lagrangian strategies for the characterization of the periodic response of a mechanical system subject to unilateral contact constraints. The model used for evaluation is an academic rod model facing an obstacle that is firstly considered as equivalent to a stiffness (flexible) and then as a rigid obstacle. Nonlinear frequency response curves are obtained through an arc-length continuation procedure and confronted to the corresponding time integration simulations. An in-depth comparative analysis is conducted on the time signals obtained through both frequency domain strategies: (1) linear complementarity problem (LCP-HBM) and (2) dynamic Lagrangian frequency time (DLFT-HBM). The unilateral contact conditions are thoroughly investigated in the time domain and compared with the reference time integration simulations. Particular attention is paid to the relation between both methods and it is shown that the DLFT-HBM is asymptotically equivalent to the LCP-HBM. This study also shows that the oversampling of time signals inside alternating frequency–time procedures generates non-physical high harmonics. Finally, a convergence analysis is conducted in order to assess the influence of the different numerical parameters on the respect of the unilateral contact laws. •In-depth comparison of two Harmonic Balance Method (HBM) based strategies.•Demonstration of the applicability of Lagrangian HBM to vibro-impact problems.•Investigation of simulated contact laws.•Insights on oversampled Alternating Frequency Time procedures for nonsmooth cases.•Proof of an asymptotic relation between the two presented HBM strategies.