Structurally transmitted dynamic power in discretely joined damped component assemblies

Abstract

In this paper, a formulation for computing the vibration transmitted among components joined at discrete locations is presented. The formulation is based on a component modal synthesis approach. Natural frequencies and modes of individual components subject to specific boundary conditions at joint locations are used to compute the modal properties of assemblies from a variational formulation. Lagrange multipliers are used to enforce constraints that motions of components be identical at joint locations, and the assembly forced response is obtained from the normal mode method. Since the Lagrange multipliers used to enforce the motion constraints are equal to the interfacial forces, evaluating these from the assembly response provides an efficient means for computing the dynamic forces and moments at joints and the mechanical power transmitted among components. The formulation is initially developed for proportionally damped assemblies. Because localized damping at joint locations is often the most significant source of damping in component assemblies, the modal synthesis and vibration transmission formulations are subsequently extended to structures with arbitrary viscous damping. Simple illustrative examples of proportionally damped and nonproportionally damped assemblies of lumped parameter systems are included.