Coulomb friction effect on the forced vibration of damped mass–spring systems

• Published in: Journal of sound and vibration Vol. 535
• Main Authors: Marino, Luca, Cicirello, Alice
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 29.09.2022
• Subjects: Friction; Harmonic excitation; Modal damping; Multi degree of freedom; Resonant behaviour; Steady-state response; Multi degree of freedom; Modal damping; Steady-state response; Resonant behaviour; Friction; Harmonic excitation
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2022.117085

This paper aims at assessing the effect of dry friction on the dynamic behaviour of a damped mechanical system subject to harmonic forcing. Previous work on friction damped systems highlighted that not including other forms of damping in the dynamic analysis can lead to unrealistic results such as the presence of infinite resonances. In this contribution, an exact solution is derived for the continuous steady-state response of multi-degree-of-freedom systems with a contact between one of the masses and an external wall, using Coulomb’s law to model the friction force and a modal damping model to account for the system’s damping. Closed-form expressions are also derived for the amplitude and phase of the continuous responses, while stick–slip responses are investigated by using an ad-hoc numerical approach. In addition, analytical and numerical results are used for exploring the features and the motion regimes of the dynamic response, leading to the following conclusions: (i) system’s damping has a limited effect on low- and high-frequency behaviours, on the presence of invariant points and inversions across the transmissibility curves and can therefore be neglected, in non-resonant conditions, in the analysis of structures where dry friction is the main source of dissipation; (ii) when the damping of the system is accounted for in the mechanical models along with Coulomb damping, finite resonant peaks are also obtained in continuous sliding regime and their amplitude decreases linearly with the friction force generated in the contact. [Display omitted] •Closed-form solution for the continuous steady-state time response, amplitude and phase.•Numerical validation of the analytical results and investigation of the stick–slip responses.•The damping of the system has a limited effect on invariant points, low- and high-frequency behaviours.•Resonant amplitudes are finite and decrease linearly with Coulomb damping.