Optimum absorber parameters for various combinations of response and excitation parameters

TLDR

Vibration absorbers for complex systems can be treated as equivalent single‑degree‑of‑freedom systems when natural frequencies are well separated, and minimizing displacement response to harmonic force has been the focus of prior work. This study derives simple expressions for optimum absorber parameters for undamped one‑degree‑of‑freedom main systems under harmonic and white‑noise excitations, with force or frame‑acceleration inputs, aiming to minimize various response measures. The authors numerically investigate the requirement of well‑separated natural frequencies and the influence of main‑system damping, and use these results to formulate the derived expressions. The resulting expressions enable determination of optimum absorber parameters for complex systems when optimization targets absolute rather than relative response quantities.

Abstract

Abstract In recent papers the author has shown that when determining optimum parameters for an absorber which minimizes the vibration response of a complex system, the latter may be treated as an equivalent single degree‐of‐freedom system if its natural frequencies are well separated. Emphasis was on minimizing the displacement response when the excitation was a harmonic force. In the present paper simple expressions for optimum absorber parameters are derived for undamped one degree‐of‐freedom main systems for harmonic and white noise random excitations with force and frame acceleration as input and minimization of various response parameters. These expressions can be used to obtain optimum parameters for absorbers attached to complex systems provided that optimization is with respect to an absolute, rather than a relative, quantity. The requirement that the natural frequencies should be well separated is investigated numerically for the different cases. The effect of damping in the main system on optimum absorber parameters is investigated also.