<p>Vibration attenuation in lightweight and flexible structures requires solutions other than conventional methods that typically result in substantial mass addition. The use of smart materials, particularly piezoelectric materials, has been one of the most commonly employed alternatives. Piezoelectric shunt damping via linear circuits (e.g. resistive-inductive) and switching circuits (e.g. synchronized switch on inductor) have been extremely well studied for suppressing resonant vibrations in flexible structures. Both analog circuits and synthetic impedance circuits with digital control have been explored for linear concepts. In a parallel body of work, from the domain of mechanical methods of vibration absorption, it is also known that leveraging nonlinearities (e.g. stiffness nonlinearity) can enhance the frequency bandwidth and offer amplitude-dependent suppression over a range of frequencies. This work combines nonlinear absorption with synthetic impedance-based piezoelectric shunt damping. Specifically, the nonlinear synthetic impedance circuit exhibits a nonlinear inductance component, with a remarkable authority to modify both the linear and nonlinear coefficients of the absorber circuit. Experiments are then performed on a cantilever with piezoelectric laminates under based excitation using an electrodynamic shaker. Piezoelectric laminates that are connected in series are shunted to a nonlinear synthetic impedance circuit. First, linear frequency response functions of the cantilever are obtained for the short-circuit and open-circuit scenarios. Linear inductive-resistive shunt damping is done next for a range of resistive loads to confirm the standard linear behavior and model parameters (for analytical and numerical simulations). Nonlinear experiments are conducted next after introducing nonlinear inductance to the shunt circuit. Base excitation experiments (up and down sine sweep) are performed for different amplitudes to explore the resulting nonlinear dynamics. Tip vibration to base motion transmissibility frequency response of the cantilever is measured along with piezoelectric voltage to base motion frequency response for a range of base excitation levels. The distortion of the frequency response curves with increased base acceleration levels is observed. Coefficients of the nonlinear shunt circuit are those of the cubic flux linkage, linear inductor, and linear resistor. These coefficients are then varied within a parameter space in a set of simulations and experiments. For instance, for a given linear and cubic inductance combination, the resistor (for dissipation) is altered to understand its effect on nonlinear absorption. Finally, the cubic nonlinear coefficient is varied to alter the manifestation of nonlinear absorption from a given base excitation intensity range to another range as a flexibility in tunning the triggering of the nonlinearity to a given excitation level.</p>

Programmable Nonlinear Vibration Absorber Using Synthetic Impedance Circuits

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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