The effects of shear deformation and rotary inertia on the electrical analogs of beams and plates for multimodal piezoelectric damping

Abstract

AbstractAnalogous electrical networks were previously derived from the Euler–Bernoulli and Kirchhoff–Love theories to represent beams and plates, respectively, for use in multimodal structural vibration damping. However, these networks do not account for shear deformations or rotary inertia, which can result in suboptimal vibration damping performance when used on moderately thick beams and plates. In this paper, we investigate the incorporation of shear deformation and rotary inertia using Timoshenko–Ehrenfest beam theory and Mindlin–Reissner plate theory to develop improved electrical networks that can more accurately represent thick beams and plates. Our findings suggest that the inclusion of shear deformation and rotary inertia can significantly improve the frequency coherence of the electrical networks and multimodal vibration damping for thicker structures. The electrical analogs presented here are of use for various applications, especially to conveniently design complex circuit topologies in fields spanning from vibration attenuation to energy harvesting.