A STUDY OF THE VIBRATIONAL ENERGIES OF 2 COUPLED BEAMS BY FINITE-ELEMENT AND GREEN-FUNCTION (RECEPTANCE) METHODS

The behaviour of two hinged-hinged beams, point coupled by springs (translational, rotary and a combination of both) with weak to strong coupling is studied from the point of view of vibrational energies, input power and power transferred through the coupling. Two configurations are studied: in the first case the beams are placed parallel to each other and only the transverse, Euler-Bernoulli modes are considered; the second configuration is more complicated with the beams placed perpendicular to each other, executing axial as well as transverse vibrations. These models are studied by using a finite element analysis (FEA) package and, alternatively, via the modally derived Green functions of the uncoupled subsystems. In both cases the beams are given proportional damping and one of the beams is driven by a point harmonic Force. The effects of coupling stiffness and modal summation bandwidth are studied. It is shown that there is good agreement between the FEA and the Green function approach over a range of coupling strengths. but that at higher strengths the number of uncoupled modes used significantly affects the accuracy of the Green Function method used here. The beams in the second configuration are then further studied from the point of view of SEA coupling loss factors. The frequency averaged coupling loss factors are caclulated for weak and strong coupling, first by using a power injection method. where the power balance equations are formed on the assumption of only direct coupling loss factors. Then, the entire matrix of direct and indirect coupling loss factors is derived by using a deterministic modal approach. These are compared and the indirect coupling loss factors are Found to be significant in magnitude in respect to the direct coupling loss factors. Several cases are studied in which the coupling powers and energy levels are predicted by using only the direct coupling loss factors and compared with the exact results obtained by using both direct and indirect factors, These agree only under certain conditions for weak coupling and show rather poorer agreement in the case of strong coupling. This behaviour demonstrates the importance of taking into account indirect coupling loss factors in SEA models having several subsystems.