The objective of this paper is to derive an approximate closed-form solution to the H∞ optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits in the presence of damping in the primary structure. To this end, the homotopy perturbation method (HPM) is utilized in which the zero-order solution is the recently-developed exact solution for an undamped primary system. Simplified, though accurate, expressions for the optimum frequency and damping ratios are also provided.
Soltani, P., Kerschen, G., Tondreau, G., & Deraemaeker, A. (2017). Tuning of a piezoelectric vibration absorber attached to a damped structure. Journal of Intelligent Material Systems and Structures, 28(9), 1115–1129. https://doi.org/10.1177/1045389X16666180