General Motion of Impact Dampers

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Abstract
The exact solution of the general steady‐state response of a sinusoidally excited primary system provided with an impact damper is derived analytically by treating the motion of the system as a piecewise linear process. The asymptotically stable regions of the resulting multivalued solutions are determined. Experimental investigations using an electronic analog computer in addition to numerical studies on a digital computer are described, and it is shown that the predictions of the theory are verified. The effects of viscous damping, frequency ratio, mass ratio, coefficient of restitution, clearance ratio, and initial conditions on the response and stability of the system are discussed, and optimum response curves over a wide frequency band are presented. The findings of this study are significantly different, both quantitatively and qualitatively from those of a recent investigation of impact dampers.

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