Study on added damping due to resistive shunting on cantilever, simply supported beam, and effect on the variation of amplitude at resonance

Abstract

The current work determines the piezoelectric damping of resistively shunted beams induced by resistors through joule heating. To predict this damping, a piezoelectric patch [Formula: see text] is attached to the surface of a cantilever beam. The current work emphasizes the effect of various parameters on damping added to the cantilever beam through the energy dissipation approach. This work analyzes different methods for predicting added damping. Results from different approaches rely on the base structure modeshape. Using the energy dissipation method from voltage generation, estimated added damping, included a stepped beam model to account for the curvature of the beam with PZT. Further, the same is validated with existing literature and found to be consistent. With the energy dissipation approach, including the stepped beam model compared with experimental literature data, the accuracy of the adopted beam model is validated. Few critical observations were made, such as the location of the PZT patch plays a vital role in determining the required added damping for a particular mode. This optimal location was the nodal location of the other modes. The location of the piezoelectric patch is an important parameter to achieve the required added damping for a particular mode. The optimal location of PZT to achieve maximum added damping for a particular mode may lie at the nodal location of other modes. This optimal location is addressed by rigorous experiments on a simply-supported beam initially and further correlated to a cantilever beam with the help of an energy dissipation approach. The energy dissipation model is correlated and validated for cantilever beam straight PZT on cantilever beams and a simply supported beam. In practical situations, in ambient conditions, environmental effects may result in a change of resonant frequency and thus amplitude. This variation may alter the base and shunt damping performance attributed to air damping. We have experimentally investigated the influence of air damping for base damping (inherent) and added damping (PZT).