New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

• Published in: Journal of sound and vibration Vol. 406; pp. 295 - 327
• Main Authors: Rahman, Md. Saifur, Lee, Yiu-Yin
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 13.10.2017; Elsevier Science Ltd
• Subjects: Algebra; Axial forces; Differential equations; Double beam; Formulations; Harmonic balance; Harmonic balance method; Large amplitude forced vibration; Nonlinear dynamics; Nonlinear equations; Structural engineering; Vibration; Nonlinear dynamics; Double beam; Large amplitude forced vibration; Harmonic balance
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2017.06.017

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined. •A new modified harmonic balance method is introduced in this study•The proposed method can generate the higher level nonlinear solution neglected by a previous method•In many previous works of double beam, the structural nonlinearity is not considered•The structural nonlinear behaviours and effects of various parameters are studied.•The linear beam resonance not considered in single beam models imposes a large effect on the nonlinear beam vibration.