Steady-State Response of a Multidegree System With an Impact Damper

Abstract

An exact solution is presented for the steady-state motion of a sinusoidally excited n-degree-of-freedom system that is provided with an impact damper. Both the excitation and the damper may be independently applied to any point in the system. Experimental studies with an analog computer and with a mechanical model corroborate the theoretical results. Results of the analysis are applied to the lumped parameter representation of a modern 10 story building, and the effects of various system parameters, including mode shape, excitation frequency, damper location, and force location are determined. It is found that the impact damper is an efficient device for reducing the vibrations of multidegree-of-freedom systems, particularly in structures such as tall buildings.