Jerry E. Farstad
Rajendra Singh
Acoust. and Dynamics Lab., Dept. of Mech. Eng., Ohio State Univ., 206 W 18th Ave., Columbus, OH 43210
Damping ratios of assembled machine structures are often significantly greater than those of the individual components from which they are assembled due to friction at the joints. In this paper, the effects of localized interfacial damping on vibration transmitted through joints in assemblies is examined. An analytical formulation based on a component modal synthesis approach is used. Because damping is concentrated at joint locations, the modes of assembled structures may be complex-valued. Consequently, a new modal synthesis formulation that permits the use of complex-valued component modes is developed. Assembly modal properties are obtained from a variational formulation in which the motion constraints at joint locations are enforced using Lagrange multipliers, which are equal to the interfacial forces and moments. Computing these from the assembly response provides an efficient means for calculating the mechanical power transmitted through the joints. An example case of an assembly of two lumped parameter oscillators connected by two joints is examined. The results indicate that localized damping has significant effects on transmitted vibration, with the effects being most significant at the higher frequencies and near the assembly natural frequencies. The effects of the relative magnitudes of damping coefficients at each joint on vibration transmitted through each are also examined.