In this paper, an analytical approach was used to formulate for gathering energy from ambient sources of vibrations. The apparatus consists of a cantilevered beam harvester with a piezoelectric patch. A coupled electromechanical modal model based on Euler–Bernoulli theory is used. The governing equations were extracted using Hamilton’s principle and then were discretized by using the Rayleigh–Ritz approach. The expected value of the electrical power output was obtained for a weakly stationary, Gaussian bandpass with zero mean base excitation. Next, a numerical solution for the beam under band-limited ambient random acceleration as the input was calculated and validated by experiment. The numerical results closely correlated to the experimental data with a deviation of about 10%.