Dynamic response of MDOF mechanical systems with contact and friction.

The interest for contact and friction vibrations of MDOF systems is two-fold: (i) a wide range of practical problems involve bodies colliding and sliding with one another; and (ii) the complex dynamics of such problems is a good testing bench for nonlinear theories. Contact modeling is a crucial challenge in the problem at hand. In this connection, contact rigidity is a quite popular assumption; unfortunately it does not allow to simulate the actual dissipative character of the multibody interactions. Indeed, the dissipation phenomena exhibited during the contact phases can be correctly described via deformable contact approach. To this end, in this paper, a refined hysteretic contact force-relative displacement relation has been formulated in order to represent contact behaviour in normal direction with respect to the interacting surfaces; moreover friction force has been assumed to depend on either relative displacement or relative velocity. Aim of the present paper is to study the dynamic response of non-smooth MDOF systems which exhibit both theoretical and practical interest, namely combined friction-contact SDOF oscillator and trilith. In more detail, SDOF oscillator is very important in understanding systems in which there are just few interacting components and it is to be hoped that much of the behaviour will also be seen in more complex systems. Moreover, the analysis of large complicated systems is not likely to proceed very far without the conceptual insights that simpler systems can provide. For instance, monumental structures are made of many blocks and the trilith is the simplest scheme of a colonnade belonging to a temple. As far as SDOF oscillators are concerned, an effort is made in this paper to lighten the behaviour of these systems colliding with an obstacle and excited by a harmonic driving force and/or by a moving base, which transfers energy to the system via friction. The different nature of discontinuities arising in the combined problem of friction and contact has been recognized and discussed. Closed-form and numerical solutions are presented for the system response. As far as the trilith is concerned, the conditions for rest or transient up to failure (overturning or sliding) have been analyzed, when the three block assembly is subjected to horizontal harmonic ground motion.