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.