Session: SYMP 3-4: Programming and Modeling

Paper Number: 140479

140479 - Piezoelectric Structures With Nonlinear Synthetic Impedance Shunts, Machine Learning-Based Simulations, and Experimental Validations 

We explore synthetic impedance-based piezoelectric structures by introducing nonlinearities in the circuit domain, along with experimental validations and machine learning-based electromechanical simulations. First, we introduce a Duffing oscillator by means of a cubic synthetic inductance. The synthetic Duffing circuit is used as a nonlinear shunt circuit for a mechanically linear piezoelectric cantilever, and it is shown that the cubic nonlinearity can be introduced and programmed by varying the respective gain in the synthetic impedance circuit to change the bandwidth and bifurcation points in the frequency response. The next step following the hardening and softening Duffing oscillator cases is the nonlinear energy sink (NES) implementation for wideband vibration attenuation without a preferential linear resonance in the shunt. A nonlinear electromechanical model is developed, and numerical simulations are performed via time-domain solutions as well as approximate analytical solution using the method of harmonic balance. Then, we present a novel and alternative model simulation approach using machine learning for enhanced computational efficiency compared to the aforementioned methods, which may be useful for design and analysis of the proposed nonlinear shunts. Specifically, we model the nonlinear vibration frequency response of the shunted piezoelectric beams using machine learning. Since an analytical solution is not available for such systems considering their nonlinearity, time-domain numerical simulations using the Runge-Kutta method and approximate analytical solution using the method of harmonic balance are some of the mostly used in simulating the response of such systems. However, as both methods require numerical analysis (Newton-Raphson method in case of harmonic balance), the process of simulating the response of the system can be computationally lengthy, especially with lightly-damped systems. The proposed approach of modeling the nonlinear vibration frequency response of the system using machine learning aims at solving the issue of lengthy computations as well as possible instabilities. An analysis of the nonlinear response of the system typically reveals the presence of distinct regions where the system exhibits two contrasting behaviors due to the basins of attractions, namely the high amplitude and low amplitude responses. The system experiences bifurcation in behavior in the up and down frequency sweep, leading to discontinuities in its response curves, with multiple bifurcation points. The discontinuous frequency response behavior becomes significantly more intricate when investigating the effect of altering the excitation amplitude or the electrical shunt considering hardening and softening scenarios as well as the amount of the cubic nonlinear inductance with the jump phenomenon. Traditional approaches, such as linear regression using a polynomial model, are inadequate in capturing the abrupt changes due to the jump phenomena observed at these bifurcation points. Therefore, a more sophisticated artificial neural network (ANN) model is explored here for the purpose of accurately modeling the response of this nonlinear electromechanical system. Following the same approach, we train an ANN model for predicting the nonlinear vibration frequency response of the stiff beam shunted to the NES for a wide range of the nonlinear cubic inductance in the NES. Results are validated against experimental measurements and computational efficiency comparisons are provided.

Presenting Author: Obaidullah Alfahmi King Abdulaziz University

Presenting Author Biography: 

Authors:

Obaidullah Alfahmi
Alper Erturk