Vibrational Energy Flows between Two Plates Forming an ‘L’-Shape and Joined by Compliant and Dissipative Couplings

Abstract

The transmission of energy between two coupled plates has been extensively discussed in the literature of structural dynamics. In most of these studies it is assumed that the plates are rigidly joined and that no energy dissipation occurs at the joint, i.e., conservative coupling. In most practical cases, however, the plate elements forming a complex, built-up structure are joined together by welding or fasteners which give rise to energy dissipation in the joints via various forms of friction and damping.

Previous SEA based studies of the transmission of energy through dissipative joints, modelled by springs and viscous dampers, have shown that the effects of dissipation in such joints can give rise to significant changes in the various quantities used in SEA, and in particular to the coupling loss factors used by the method. In this work, the transmission of energy through a compliant and dissipative joint between two plates forming an ‘L’ -shape is investigated, using a receptance approach. The two plates are assumed to be thin, homogeneous and isotropic. Their common edge is taken to be simply supported so that the joint has relative motions only in its rotational degree of freedom, i.e., translation normal to the plate at the common edge is not permitted. The joint is then assumed to have a constant complex stiffness per unit length, denoted by K +iωγ (Nm per m radian). Exact formulae for the spectral densities of the energy flow through the joint, the energy dissipated at the joint and the power input into the plates are established for the case of excitation by random ergodic forcing.

The aim of this study is to examine the effects of the joint damping and compliance on the magnitudes of the energy flows through the joint and the energy levels in the two plates. Interest is focused on the power dissipated at the joint and the conditions under which this quantity is maximised. The coupling and coupling damping loss factors that would be used in an SEA model of this problem are also derived, using the power injection method. These are compared to the results obtained from using a wave based approach with semi-infinite subsystem modles