Piezoelectric materials have been extensively employed in small scale energy harvesting devices. Commonly, the ambient excitation in these energy harvesting systems is considered to be harmonic. While in practical cases, these excitations are random in nature. The objective of the current paper is to use random vibration theory to investigate energy harvesting from a clamped circular plate interconnected to a circular piezoelectric layer. The excitations are assumed to be a random uniform pressure applied to the plate resulted from an acoustic wave and a random base acceleration of the system. Lagrange equations are utilized to derive the coupled equations describing the dynamic behavior of the plate and the circuit voltage. The random inputs are assumed to be band-limited uncorrelated white noises. Using the random vibration theory, the statistical parameters describing the plate’s dynamic and the harvested voltage are derived in terms of random characteristics of the inputs. A parametric study is carried out to investigate the effect of different design parameters on the harvested power. Also, an optimization problem is solved for maximizing the power density in the system. Using the results of the optimization problem, the power density can be significantly improved up to 3.2 mW/m 2 . The quantitative and qualitative results obtained in this paper can be effectively used for the optimal design of other piezoelectric energy harvesters under stochastic excitations.

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