Optimal design of energy harvesting from vibration subject to stochastic colored Gaussian process

The problem treated in this paper is the optimal electromechanical setting of energy harvesters working with vibrations of random nature. We consider a simple system composed of two parts; one electrical circuit with a mechanical single-degree-of-freedom system, coupled to a piezoelectric element. The electric circuit is modeled as a simple one, composed of a resistance and a capacity only, while a linear viscoelastic model is used for the mechanical element. The only joint electro and mechanical element is the piezoelectric device, which is controlled by both the mechanical velocity and the electrical tension. This scheme is treated as dimensionless using the random vibration theory since the base excitation is considered as a stationary white noise Gaussian process. To consider the non-uniform frequency content, that characterizes many real vibration phenomena, the input is properly colored using simple linear filters. System response statistics is evaluated by covariance approach, producing both covariance matrix of system parameters and mean value of electric power under different filters and systems configurations. The optimal ratio between the periods of the mechanical and electric systems is thus defined maximizing the mean power value. This ratio is obtained numerically for some test cases in a graphic representation to evaluate the sensitivity response to selected parameters.