Abstract
Piezoelectric (PZT) shunt damping is an effective method to dissipate energy from a vibrating structure; however, most of the applications focus on targeting specific modes for structures vibrating at low-frequency range, i.e. deterministic substructure (DS). To optimally attenuate structures vibrating at high-frequency range, i.e. non-deterministic substructure (Non-DS) using a PZT shunt damper, it is found that the impedance of the PZT patch’s terminal needs to be the complex conjugate of its inherent capacitance paralleled with the impedance ‘faced’ by its non-deterministic host structure underline moment actuation. The latter was derived in terms of estimation of the effective line moment mobility of a PZT patch on a Non-DS plate by integrating the expression of driving point moment mobility of an infinite thin plate. This paper conducts a parametric investigation to study the effect of changing the size, quantity and configuration of the PZT patch to the performance of the optimal PZT shunt dampers in dissipating the energy of its non-deterministic host structure. Results are shown in terms of energy reduction ratio of the thin plate when attached with optimal PZT shunt damper(s).
Highlights
Piezoelectric (PZT) shunt damping is an effective method to dissipate energy from a vibrating structure; most of the applications focus on targeting specific modes for structures vibrating at low-frequency range, i.e. deterministic substructure (DS)
This paper investigates the effect of changing the size, quantity, and configuration of the PZT patch, respectively, in reducing its non-deterministic thin plate’s energy
The real and imaginary expressions of Z∞,k, that is the impedance ‘faced’ by the non-deterministic thin plate when being subjected by the excitation of line moments in rectangular/square shape distribution is derived using double integration of infinite mobility resulting to effective line moment mobility and eventually used in the expression of shunt circuit impedance, Zsh,k
Summary
Based on high-frequency vibration control which specify the range of frequency to be controlled in line with SEA context i.e. frequency with respect to MOF. An attempt to develop active control for structures vibrating at the high-frequency range has been discussed in work by Muthalif[6] where they used a skyhook damper (equivalent to point force) to dissipate energy from a non-deterministic thin plate. The PZT shunt damper’s optimal circuit impedance to maximize energy dissipation from its non-deterministic host structure (a thin plate is used) needs to be derived. This article is organized as follows; “Derivation of optimal impedance for non-DS control” section shows the mathematical derivation to obtain the optimal impedance to achieve maximum energy dissipation of a Non-DS attached with a PZT shunt damper by utilizing the Hybrid Modelling method equation. “Simulation studies on parametric investigations” section compiles simulation studies on changing the size, quantity, and connection of the optimal PZT shunt dampers, respectively, to the energy reduction ratio achieved by the non-deterministic thin plate. The equation used to find the Non-DS energy (SEA part of the hybrid method) for the system in Fig. 2 is[8]: Scientific Reports | (2021) 11:4642 |
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