Abstract
This paper investigates the steady-state response of a harmonically excited multi-degree-of-freedom (MDOF) system with a Coulomb contact between: (1) a mass and a fixed wall; (2) two different masses; (3) a mass and an oscillating base. Although discrete MDOF models are commonly used at early design stages to analyse the dynamic performances of engineering structures, the current understanding of the friction damping effects on MDOF behaviour is still limited due to the absence of analytical solutions. In this contribution, closed-form expressions of the continuous time response, the displacement transmissibility and the phase angle of each mass of the system are derived and validated numerically for 2DOF and 5DOF systems. Moreover, the features of the analytical response are investigated, obtaining the following results: (i) the determination of the minimum amounts of friction for which the resonant peaks become finite and (ii) for which stick-slip motion can be observed at high frequencies; (iii) an equation for the evaluation of invariant points for the displacement transmissibilities; (iv) a better understanding of phenomena such as the inversions of the transmissibility curves and the onset of additional resonant peaks due to the permanent sticking of the mass in contact. All these results show that MDOF systems exhibit significantly different dynamic behaviours depending on whether the friction contact and the harmonic excitation are applied to the same or different masses.
Highlights
Many engineering structures are characterised by the presence of frictional interfaces
This paper proposes analytical expressions for the steady-state response of MDOF systems with a single Coulomb friction contact subjected to harmonic excitation and an exploration of their dynamic behaviour based on these derived solutions
The main dynamic response features are presented for MDOF systems under joined base-wall excitation in what follows, referring as example to the results shown in Figs.19 and 20
Summary
Many engineering structures are characterised by the presence of frictional interfaces. This paper proposes analytical expressions for the steady-state response of MDOF systems with a single Coulomb friction contact subjected to harmonic excitation and an exploration of their dynamic behaviour based on these derived solutions. All these solutions hold for any number of DOFs and take into account harmonic and friction forces applied to different masses of the system They can be applied to the analysis of early design stages of engineering systems where MDOF models with a single contact are of interest, including the implementation of a friction damper in buildings [44], car suspensions [45], taxing of airplanes models [46] and energy harvesters [47].
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