We address the conversion of mechanical energy from low-level ambient vibration into usable electrical energy. Development of this self-renewing energy source is vital to portable electronics and wireless sensors, especially since battery development has reached a plateau over the past decade. The passive nature of the proposed energy harvesting system provides for this self-renewing energy source. Conventional vibration energy harvesting systems are often based on linear elements, requiring specific tuning to achieve resonance and, thus, acceptable performance. This tuning is based on the predominant frequency of the ambient vibration. Linear energy harvesting systems are less desirable because ambient environmental conditions such as frequency content change with time, decreasing the performance of the system. This project focuses on the unique properties of a class of strongly nonlinear vibrating systems to effectively harvest energy under several excitation conditions. These excitations include lowlevel vibration from a wide range of environmental conditions including frequency content and low-level successive impulses at various frequencies. The later excitation condition is examined in this work. Numerical simulations of the proposed model, an essentially nonlinear oscillator with purely cubic stiffness attached to a larger grounded linear oscillator, have shown capture into sustained dynamic instability from successive low-level impulsive excitations. This sustained dynamic instability results in high energy harvesting efficiency. The electromechanical coupling is realized by a piezoelectric element in the mechanical system with voltage dissipated across a resistive load in the electrical system. This study focuses on characterizing the response of the system to varying parameters, such as fundamental period of the linear oscillator, impact frequency, and impact magnitude. An optimal fundamental period and impact frequency for dynamic instability are examined in this work. Analysis of the frequency-energy relation reveals the presence of sustained dynamic instability when the system operates under these specific parameters, leading to an optimized system for experimental validification.