This paper presents a comparative study on two types of shunted piezoelectric patch adaptive vibration absorbers, which can be bonded in batches on thin-walled structures to control the broad-band resonant response of low order flexural modes. The self-contained control units are formed by a thin piezoelectric patch connected either to a series or to a parallel resistive-inductive (RL) network. The two components of the shunt are adapted online in such a way as to maximise the time-averaged electric power absorbed by the shunt, which corresponds to minimising the time-averaged total flexural response of the hosting structure. The study considers a practical demonstrator formed by a thin rectangular plate with five piezoelectric patches connected to digital RL-shunts, which is excited in bending by a stationary white noise point force. The aim of the paper is to contrast the tuning and vibration control properties of the series and parallel RL shunts. More specifically, the online implementation of a recursive two-paths tuning strategy along R-constant and L-constant paths with an extremum seeking gradient search algorithm is analysed first for the two types of shunts. Then, the vibration control performance produced by the two types of shunts is investigated for the case where they are tuned to control the resonant response of the first flexural mode of the plate.
AndreausUPorfiriM (2007) Effect of electrical uncertainties on resonant piezoelectric shunting. Journal of Intelligent Material Systems and Structures18(5): 477–485.
2.
AriyurKBKrsticM (2003) Real-Time Optimization by Extremum-Seeking Control. Hoboken, NJ: John Wiley & Sons.
3.
BehrensSAFlemingAJMoheimaniSOR (2003) A broadband controller for shunt piezoelectric damping of structuralvibration. Smart Materials and Structures12: 18–28.
4.
BerardengoMCigadaAManzoniS, et al. (2015) ‘Vibration control by means of piezoelectric actuators shunted with LR impedances: performance and robustness analysis’. Shock and Vibration2015: 1–30. DOI: 10.1155/2015/704265.
5.
ClarkRLSaundersWRGibbsGP (1998) Adaptive structures. Dynamics and Control. New York: Wiley.
6.
Dal BoLGardonioPCasagrandeD, et al. (2019) Smart panel with sweeping and switching piezoelectric patch vibration absorbers: experimental results. Mechanical Systems and Signal Processing120: 308–325. DOI: 10.1016/j.ymssp.2018.10.024.
7.
BoLDHeHGardonioP, et al. (2022) Design tool for elementary shunts connected to piezoelectric patches set to control multi-resonant flexural vibrations. Journal of Sound and Vibration520: 116554. DOI: 10.1016/j.jsv.2021.116554.
8.
DarleuxRLossouarnBDeüJ.-F (2018) Passive self-tuning inductor for piezoelectric shunt damping considering temperature variations. Journal of Sound and Vibration432: 105–118. DOI: 10.1016/j.jsv.2018.06.017.hal-02166426.
9.
Den HartogJP (1956) Mechanical Vibrations. New York, USA: McGraw-Hill, Vol. 4th, 87–121.
10.
DochainDPerrierMGuayM (2011) Extremum seeking control and its application to process and reaction systems: a survey. Mathematics and Computers in Simulation82(3): 369–380. DOI: 10.1016/j.matcom.2010.10.022.
11.
DoschJJInmanDJGarciaE (1992) A self-sensing piezoelectric actuator for collocated control. Journal of Intelligent Material Systems and Structures3(No.1): 166–185.
12.
FahyFGardonioP (2007) Sound and Structural Vibration. Oxford: Academic Press.
GardonioPCasagrandeD (2017) Shunted piezoelectric patch vibration absorber on two-dimensional thin structures: tuning considerations. Journal of Sound and Vibration395: 26–47. DOI: 10.1016/j.jsv.2017.02.019.
15.
GardonioPTurcoE (2019) Tuning of vibration absorbers and Helmholtz resonators based on modal density/overlap parameters of distributed mechanical and acoustic systems. Journal of Sound and Vibration451: 32–70. DOI: 10.1016/j.jsv.2019.03.015.
16.
GardonioPLeeYSElliottSJ, et al. (2001) Analysis and measurement of a matched volume velocity sensor and uniform force actuator for active structural acoustic control. Journal of the Acoustical Society of America110(6): 3025–3031. DOI: 10.1121/1.1412448.
17.
GardonioPZientekMDal BoL (2019) Panel with self-tuning shunted piezoelectric patches for broadband flexural vibration control. Mechanical Systems and Signal Processing134: 106299. DOI: 10.1016/j.ymssp.2019.106299.
18.
GardonioPTurcoEKrasA, et al. (2021) Semi-active vibration control unit tuned to maximise electric power dissipation. Journal of Sound and Vibration499: 116000. DOI: 10.1016/j.jsv.2021.116000.
19.
GardonioPKonda RodriguesGDal BoL, et al. (2022) Extremum seeking online tuning of a piezoelectric vibration absorber based on the maximisation of the shunt electric power absorption. Mechanical Systems and Signal Processing176: 109171. DOI: 10.1016/j.ymssp.2022.109171.
20.
GrippJAGóesLCSHeussO, et al. (2015) An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure. Smart Materials and Structures24(12): 125017.
21.
GuYClarkRLFullerCR, et al. (1994) Experiments on active control of plate vibration using piezoelectric actuators and polyvinylidene fluoride (PVDF) modal sensors. Journal of Vibration and Acoustics116(3): 303–308. DOI: 10.1115/1.2930429.
22.
HagoodNWvon FlotowA (1991) Damping of structural vibrations with piezoelectric materials and passive electrical networks. Journal of Sound and Vibration146(2): 243–268.
23.
HøgsbergJKrenkS (2012) Balanced calibration of resonant shunt circuits for piezoelectric vibration control. Journal of Intelligent Material Systems and Structures23(17): 1937–1948. DOI: 10.1177/1045389X12455727.
24.
HøgsbergJKrenkS (2017) Calibration of piezoelectric RL shunts with explicit residual mode correction. Journal of Sound and Vibration386: 65–81. DOI: 10.1016/j.jsv.2016.08.028.
25.
HollkampJJStarchvilleTF (1994) A self-tuning piezoelectric vibration absorber. Journal of Intelligent Material Systems and Structures5(4): 559–566. DOI: 10.1177/1045389X9400500412.
26.
HorowitzPHillW (1989) The Art of Electronics. Cambridge: Cambridge University Press.
27.
IkegameTTakagiKInoueT (2019) Exact solutions to H∞ and H2 optimizations of passive resonant shunt circuit for electromagnetic or piezoelectric shunt damper. Journal of Vibration and Acoustics141(3). DOI: 10.1115/1.4042819.
28.
KimJRyuYHChoiSB (2000) New shunting parameter tuning method forpiezoelectric damping based on measured electrical impedance. Smart Materials and Structures9: 868–877.
29.
KodejskaMMokryPLinhartV, et al. (2012) Adaptive vibration suppression system: an iterative control law for a piezoelectric actuator shunted by a negative capacitor. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control59(12): 2785–2796.
30.
Konda RodriguesGGardonioPDal BoL, et al. (2022) Piezoelectric patch vibration control unit connected to a self-tuning RL-shunt set to maximise electric power absorption. Journal of Sound and Vibration536: 117154.
31.
Konda RodriguesGGardonioPDal BoL, et al. (2022) Multimodal vibration control with piezoelectric patches connected to self-tuning RLC shunts. Mechanics of Advanced Materials and Structures30: 1050–1063. DOI: 10.1080/15376494.2022.2136806.
32.
KrstićM (2000) Performance improvement and limitations in extremum seeking control. Systems & Control Letters39(5): 313–326. DOI: 10.1016/S0167-6911(99)00111-5.
OgawaMTakagiKJikuyaI, et al. (2014) Adaptive piezoelectric shunt damping by self-tuning negative capacitor. Transactions of the JSME (in Japanese)80(820): DR0382.
35.
MattenGColletMSadoulet-ReboulE, et al. (2013) Sensitivity analysis and control of a cantilever beam by mean of a shunted piezoelectric patch. 1st Euro-Mediterranean Conference on Structural Dynamics and Vibroacoustics (MEDYNA 2013), Paris, France, 2013.
36.
NiederbergerDMorariM (2006) An autonomous shunt circuit for vibration damping. Smart Materials and Structures15(2): 359–364.
37.
RazaviB (2020) The active inductor [A circuit for all seasons. IEEE Solid-State Circuits Magazine12(2): 7–11.
38.
RazeG (2021) Piezoelectric Digital Vibration Absorbers for Multimodal Vibration Mitigation of Complex Mechanical Structures. PhD thesis. Liège, Belgium: Liège Université Sciences Appliquées.
39.
SoltaniPKerschenGTondreauG, et al. (2014) Piezoelectric vibration damping using resonant shunt circuits: an exact solution. Smart Materials and Structures23(12): 125014.
40.
SumaliHMeissnerKCudneyHH (2001) A piezoelectric array for sensing vibration modal coordinates. Sensors and Actuators A: Physical93(2): 123–131. DOI: 10.1016/S0924-4247(01)00644-6.
41.
TanY (2010) Extremum seeking from 1922 to 2010Proceedings of the 29th Chinese Control Conference, Chongqing, China, 28-30 May 2010.
42.
ThomasODucarneJDeüJ.-F (2011) Performance of piezoelectric shunts for vibration reduction. Smart Materials and Structures21(1): 015008.
43.
ToftekærJFBenjeddouAHøgsbergJ, et al. (2018) Optimal piezoelectric resistive-inductive shunt damping of plates with residual mode correction. Journal of Intelligent Material Systems and Structures29(16): 3346–3370. DOI: 10.1177/1045389X18798953.
44.
ToftekærJFBenjeddouAHøgsbergJ (2020) General numerical implementation of a new piezoelectric shunt tuning method based on the effective electromechanical coupling coefficient. Mechanics of Advanced Materials and Structures27(22): 1908–1922.
45.
WuS (1996) Piezoelectric shunts with a parallel R-L circuit for structural damping and vibration control. In Smart Structures and Materials 1996: Passive Damping and Isolation, San Diego, California, 26-27 February 1996. DOI: 10.1117/12.239093.
46.
YamadaKMatsuhisaHUtsunoH, et al. (2010) Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements. Journal of Sound and Vibration329(24): 5036–5057.
