Reduced order models for nonlinear dynamic analysis of structures with intermittent contacts

Abstract

The forced response of structures with complex geometry and intermittent contacts is nonlinear due to contact breathing phenomena that occur during vibration. Therefore, calculation times to predict such responses can be extremely long especially because highly refined finite element models are necessary to properly model geometrically complicated structures. To alleviate this issue, reduced order models can be very beneficial as they can dramatically speed up the analysis process by reducing the size of the system and thus the calculation times. In this paper, a reduced order modeling method for the forced response of structures with intermittent contacts is developed. The proposed approach assumes that the dynamics of the nonlinear system in the frequency range of interest is spatially correlated. The spatial correlation can be dominated by normal modes of the open (or sliding) linear system. Nonetheless, the boundary conditions of a vibrating structure with intermittent frictionless contacts vary in time (i.e. at any time t the contacts are partly open and closed), and the actual extent of the contact area changes over time. Here, this observation is complemented by the assumption that, given the frequency range of the harmonic excitation force, the system dynamics is dominated by one of the modes of either the open or the sliding system, and thus the time evolution of the contact area can be estimated by knowing (a) the normal penetration at the contact node pairs at rest due to pre-stress, and (b) the vector of normal relative displacements at the contact nodes of that dominant mode. As a result, a set of normal modes – referred to as piecewise linear modes – is computed, by imposing special boundary conditions at the nodes lying on the contact surfaces, and a reduction basis is selected and used to reduce the size of the model of the system. Two numerical test cases, specifically a cracked plate and two coaxial cylinders are used for validation. Results show that the proposed method allows to accurately compute the nonlinear forced response of structures with intermittent contacts both in case of zero gap and in case of initial pre-stress at the contacts.