Electrical Equivalent Circuit of Multi-mode Flexible Beams with Piezoelectric Elements

Surface mounted piezoelectric sensors and actuators on elastic structures are often connected to electrical networks. The coupled equations of motion of the elastic structure with piezoelectric elements are already well known. However, due to complex behavior of some electrical elements in the electrical network, it is not an easy task to obtain the integrated equations of the whole system. A good remedy for this problem is to take advantage of an equivalent electrical circuit (EEC) representation of the mechanical part, leading the entire system to be represented as an electrical circuit. In this study, the authors propose a new method for constructing the EEC. This method is based upon the multimode analysis of vibrating structures. Utilizing modal analysis, the equations are converted to tridiagonal form which is shown to be appropriate for constructing the EEC. In contrast to previous works, no restrictive approximations are made in its development. This method can also be used in similar applications, such as power harvesting from vibrating structures.