An active actuator of electro-active polymer (EAP), i.e. ionic polymer metal composite (IPMC), is subjected to alternating electric potential to investigate and study the time-delayed vibration characteristics. A generalized mathematical model of the actuator is obtained assuming multi-mode excitation and applying the Hamilton's principle. Lambert W-function is then applied and a closed form solution of the transcendental characteristic equation of delay differential equation (DDE) is obtained. Delay differential equations (DDEs) are then solved taking into account the experimental data and physical properties of IPMC, and the results are discussed and validated.