Jerry E. Farstad
Dept. of Mech. Eng., Ohio State Univ., 206 W. 18th Ave., Columbus, OH 43210
In many cases, the most practical approach for reducing noise in built-up machine assemblies is to reduce the vibration transmitted through joints to the machine housing as much as possible. In this paper, a new analysis framework for estimating the vibration transmitted among machine components joined at discrete locations in vibrating assemblies is presented. The method is based on a recently developed modal synthesis approach. Natural frequencies and modes of the disassembled components subject to specific boundary conditions applied at the joint locations are used to compute the natural frequencies and modes of the assembly from a variational formulation. Lagrange multipliers are used to enforce the constraints that motions of components at joint locations be identical. The modal properties of the assembly are then used to compute its forced response. Since the Lagrange multipliers used to enforce the constraints represent the interfacial joint forces, evaluating these from the forced response provides an efficient way of computing the dynamic power transmission among components, which is probably the best measure of transmitted vibration. In addition to theory, a simple example of an assembly of two lumped parameter systems is included.