The linear 3D piezoelasticity theory along with active damping control (ADC) strategy are applied for non-stationary vibroacoustic response suppression of a doubly fluid-loaded functionally graded piezolaminated (FGPM) composite hollow cylinder of infinite length under general time-varying excitations. The control gain parameters are identified and tuned using Genetic Algorithm (GA) with a multi-objective performance index that constrains the key elasto-acoustic system parameters and control voltage. The uncontrolled and controlled time response histories due to a pair of equal and opposite impulsive external point loads are calculated by means of Durbin’s numerical inverse Laplace transform algorithm. Numerical simulations demonstrate the superior (good) performance of the GA-optimized distributed active damping control system in effective attenuation of sound pressure transients radiated into the internal (external) acoustic space for two basic control configurations. Also, some interesting features of the transient fluid-structure interaction control problem are illustrated via proper 2D time domain images and animations of the 3D sound field. Limiting cases are considered and accuracy of the formulation is established with the aid of a commercial finite element package as well as comparisons with the current literature.