A piezo-metastructure with bistable circuit shunts for adaptive nonreciprocal wave transmission

In this paper, we present a piezo-metastructure shunted with bistable circuits to achieve adaptive nonreciprocal elastic wave transmission. Static properties of the bistable circuit are first investigated, followed by numerical investigation of wave transmission characteristics on the nonlinear piezo-metastructure. Both the local-resonance bandgap and the bandgap transmission phenomenon, also known as supratransmission, are explored and investigated. By introducing circuit asymmetry, the supratransmission thresholds, critical excitation amplitudes to enable bandgap transmission, are found at different levels for the different wave transmission directions and hence creating an excitation amplitude range within which nonreciprocal wave transmission can be facilitated. Effect of the asymmetry factor on nonreciprocity properties is subsequently analyzed and the trade-offs between the forward transmission amplitude and the range of excitation with nonreciprocity are identified. Additionally, it is demonstrated that wave transmission characteristics of the proposed nonlinear piezo-metastructure can be adaptively tuned by conveniently adjusting stable equilibria of the bistable circuit. Lastly, the observed wave transmission properties are further corroborated by experimental investigations. Overall, the results illustrate a novel means to manipulate unidirectional elastic wave transmission using a nonlinear piezo-metastructure.

[1]  Michael J. Frazier,et al.  Band gap transmission in periodic bistable mechanical systems , 2017 .

[2]  Paolo Ermanni,et al.  Phononic Crystal with Adaptive Connectivity , 2014, Advanced materials.

[3]  O. Bilal,et al.  Bistable metamaterial for switching and cascading elastic vibrations , 2017, Proceedings of the National Academy of Sciences.

[4]  Kon-Well Wang,et al.  Adaptive Structural Systems with Piezoelectric Transducer Circuitry , 2010 .

[5]  Kon-Well Wang,et al.  Harnessing Bistable Structural Dynamics: For Vibration Control, Energy Harvesting and Sensing , 2017 .

[6]  J Leon,et al.  Energy transmission in the forbidden band gap of a nonlinear chain. , 2002, Physical review letters.

[7]  John William Strutt,et al.  Some General Theorems relating to Vibrations , 1871 .

[8]  R. Fleury,et al.  Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator , 2014, Science.

[9]  K. W. Wang,et al.  Enhancing Structural Damage Identification Robustness to Noise and Damping With Integrated Bistable and Adaptive Piezoelectric Circuitry , 2015 .

[10]  Giulio Casati,et al.  Asymmetric wave propagation in nonlinear systems. , 2011, Physical review letters.

[11]  M. Ruzzene,et al.  An investigation of electroelastic bandgap formation in locally resonant piezoelectric metastructures , 2017 .

[12]  Kon-Well Wang,et al.  Predicting non-stationary and stochastic activation of saddle-node bifurcation in non-smooth dynamical systems , 2018 .

[13]  G. Theocharis,et al.  Bifurcation-based acoustic switching and rectification. , 2011, Nature materials.

[14]  Manuel Collet,et al.  Enhancement of elastic wave energy harvesting using adaptive piezo-lens , 2017 .

[15]  Yeshaiahu Fainman,et al.  Nonreciprocal Light Propagation in a Silicon Photonic Circuit , 2011, Science.

[16]  M. Ruzzene,et al.  A general theory for bandgap estimation in locally resonant metastructures , 2016, 1612.03130.

[17]  Umesh Kumar,et al.  Analytical Study of Inductor Simulation Circuits , 1989 .

[18]  Giorgio Rizzoni,et al.  Fundamentals of Electrical Engineering , 2008 .

[19]  Andrea Alù,et al.  Fundamental bounds on the operation of Fano nonlinear isolators , 2018 .

[20]  Yi-Ze Wang,et al.  Nonreciprocal phenomenon in nonlinear elastic wave metamaterials with continuous properties , 2018, International Journal of Solids and Structures.

[21]  Xu Guo,et al.  Frequency-Preserved Acoustic Diode Model with High Forward-Power-Transmission Rate , 2015 .

[22]  Kon-Well Wang,et al.  Electromechanical impedance-based damage identification enhancement using bistable and adaptive piezoelectric circuitry , 2018, Structural Health Monitoring.

[23]  Liqun Chen,et al.  Frequency-preserved non-reciprocal acoustic propagation in a granular chain , 2018 .

[24]  K W Wang,et al.  Metastable modular metastructures for on-demand reconfiguration of band structures and nonreciprocal wave propagation. , 2017, Physical review. E.

[25]  Jiong Tang,et al.  Tunable prism based on piezoelectric metamaterial for acoustic beam steering , 2017 .

[26]  Massimo Ruzzene,et al.  Non-reciprocal elastic wave propagation in spatiotemporal periodic structures , 2016, 1605.00734.

[27]  Jiong Tang,et al.  Acoustic prism for continuous beam steering based on piezo-electric metamaterial , 2016, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[28]  K. W. Wang,et al.  Robust sensing methodology for detecting change with bistable circuitry dynamics tailoring , 2013 .

[29]  Kon-Well Wang,et al.  On the wave propagation analysis and supratransmission prediction of a metastable modular metastructure for non-reciprocal energy transmission , 2017, Journal of Sound and Vibration.

[30]  Chiara Daraio,et al.  Granular acoustic switches and logic elements , 2014, Nature Communications.

[31]  Bin Liang,et al.  Acoustic diode: rectification of acoustic energy flux in one-dimensional systems. , 2009, Physical review letters.

[32]  B. Liang,et al.  An acoustic rectifier. , 2010, Nature materials.

[33]  Baowen Li,et al.  Thermal diode: rectification of heat flux. , 2004, Physical review letters.

[34]  Kon-Well Wang,et al.  Enhancing Damage Identification Robustness to Noise and Damping Using Integrated Bistable and Adaptive Piezoelectric Circuitry , 2014 .

[35]  Massimo Ruzzene,et al.  Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[36]  Massimo Ruzzene,et al.  Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches , 2001 .

[37]  Mickaël Lallart,et al.  Vibration reduction for smart periodic structures via periodic piezoelectric arrays with nonlinear interleaved-switched electronic networks , 2017 .

[38]  Massimo Ruzzene,et al.  Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos , 2011 .

[39]  Kestutis Pyragas,et al.  Delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems: theory and experiment. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Guoliang Huang,et al.  Modulated phononic crystals: Non-reciprocal wave propagation and Willis materials , 2017 .

[41]  Franziska Hoffmann,et al.  Design Of Analog Cmos Integrated Circuits , 2016 .