Multi-beam piezoelectric systems by means of dynamically equivalent stiffness concept

Energy harvesting devices allow to obtain forms of energy present in nature and to convert them into electrical energy. One way of generating energy from mechanical vibrations is by using beams of piezoelectric materials. This paper proposes an alternative methodology for characterizing the dynamic behavior of a vibrating composite system composed of a cantilever steel base beam (primary system) and a piezoelectric beam attached to it. The approach involves representing the piezoelectric beam using an equivalent dynamic stiffness at its base. This simplifies the mathematical representation of the compound system and enables the system dynamics to be described solely in terms of the generalized coordinates of the primary system, which is advantageous in optimization environments where a reduced number of equations can facilitate analysis. To determine the equivalent dynamic stiffness, different mathematical models of one and multiple degrees of freedom are presented, including the description of the polyamide base of the piezoelectric sheet. An inverse problem is used to identify system parameters, and the energy generation over a wide range of frequencies is analyzed. Experimental frequency response functions of the voltage-acceleration type are obtained to validate numerical findings, demonstrating that the proposed methodology is a cost-effective alternative for parameter identification or optimal design in energy generation.