In this paper, we present a nonlinear energy harvester that is based on a "soft-mode" nonlinearity and is able to work in presence of a truly random excitations. The proposed harvester is configured with a cantilever beam structure, and, at the tip is a cylindrical container filled with freely moving iron balls. The nonlinearity is implemented through the container, as a piecewise function. This structure, in presence of noise, can be assumed as a second order (mass-spring-damper) nonlinear system where the length of the spring changes as a function of external vibration. As will be demonstrated, this nonlinearity will improve the performance of the energy harvester under random excitation. In comparison, the conventional approach based on resonant oscillators is able to collect energy only around its mechanical natural frequency, while the solution pursued here will present a wide spectrum of response. Furthermore, the implemented nonlinearity here does not possess any barrier of potential or mechanical threshold. Because of this, it is able to work at weak signal levels and without mixture of periodic signals. A piezoelectric element has been used to convert the mechanical vibrations into an electrical signal. The system has been modeled and simulated. Experimental validations have been carried out, demonstrating the suitability of the proposed solution.