Placement and dimension optimization of shunted piezoelectric patches for vibration reduction

Abstract Passive structural vibration reduction by means of shunted piezoelectric patches is addressed in this paper. We present a strategy to optimize, in terms of damping efficiency, the geometry of piezoelectric patches as well as their placement on the host elastic structure. This procedure is based on the maximization of the modal electro-mechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunt is tuned. To illustrate the method, a general analytical model of a laminated beam is proposed. Two particular configurations are investigated: (i) a beam with two collocated piezoelectric patches connected in series or in parallel to the shunt and (ii) a cantilever beam with one patch. After a modal expansion, original closed-form solutions of the MEMCF are exhibited, which enables to compute optimal values for the placement, length and thickness of the piezoelectric patches that maximize the MEMCF. A dimensionless model is used so that this study can be used to design any smart beam, whatever be its dimensions. More general results about the coupling mechanisms between the piezoelectric patches and the host structure are also raised. In particular, it is found that the patches thickness is an essential parameter and that several configurations are possible, depending on the considered vibration mode. Experiments are also proposed to validate the model.

[1]  Seung-Yop Lee,et al.  Theoretical modeling, experiments and optimization of piezoelectric multimorph , 2005 .

[2]  Mohamed Ichchou,et al.  Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures , 2009 .

[3]  Nesbitt W. Hagood,et al.  Damping of structural vibrations with piezoelectric materials and passive electrical networks , 1991 .

[4]  G. C. Smith,et al.  Frequency-Shaping with Spatial Compensators , 2000 .

[5]  Bin Li,et al.  Vibration suppression of a hard disk driver actuator arm using piezoelectric shunt damping with a topology-optimized PZT transducer , 2009 .

[6]  Daniel J. Inman,et al.  Effect of Strain Nodes and Electrode Configuration on Piezoelectric Energy Harvesting From Cantilevered Beams , 2009 .

[7]  Dionisio Del Vescovo,et al.  Comparison of piezoelectronic networks acting as distributed vibration absorbers , 2004 .

[8]  M. Ruzzene,et al.  Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates , 2009 .

[9]  M. Morari,et al.  Structural Vibration Control via R-L Shunted Active Fiber Composites , 2007 .

[10]  M. Géradin,et al.  Mechanical Vibrations: Theory and Application to Structural Dynamics , 1994 .

[11]  Paolo Ermanni,et al.  Optimum placement of piezoelectric ceramic modules for vibration suppression of highly constrained structures , 2007 .

[12]  A. Pisano,et al.  Modeling and optimal design of piezoelectric cantilever microactuators , 1997 .

[13]  Shilin Xie,et al.  Optimal shape control of a beam using piezoelectric actuators with low control voltage , 2009 .

[14]  Ieee Standards Board.  IEEE Standard on Piezoelectricity , 1996 .

[15]  C. Davis,et al.  A modal strain energy approach to the prediction of resistively shunted piezoceramic damping , 1995 .

[16]  Jean-François Deü,et al.  Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS , 2012 .

[17]  Boris Lohmann,et al.  Vibration attenuation using a piezoelectric shunt circuit based on finite element method analysis , 2006 .

[18]  Olivier Thomas,et al.  Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients , 2009 .

[19]  M. A. Trindade,et al.  Effective Electromechanical Coupling Coefficients of Piezoelectric Adaptive Structures: Critical Evaluation and Optimization , 2009 .

[20]  Joseph J. Hollkamp,et al.  A Self-Tuning Piezoelectric Vibration Absorber , 1994 .

[21]  Mary Frecker,et al.  Recent Advances in Optimization of Smart Structures and Actuators , 2003 .

[22]  C. H. Park,et al.  Dynamics modelling of beams with shunted piezoelectric elements , 2003 .

[23]  Liviu Nicu,et al.  Determination of the d31 piezoelectric coefficient of PbZrxTi1−xO3 thin films using multilayer buckled micromembranes , 2006 .

[24]  O. Thomas,et al.  Performance of piezoelectric shunts for vibration reduction , 2011 .

[25]  G. Caruso.  A critical analysis of electric shunt circuits employed in piezoelectric passive vibration damping , 2001 .

[26]  Sebastien Hentz,et al.  Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films , 2009 .

[27]  Balakumar Balachandran,et al.  Nonlinear oscillations of piezoelectric microresonators with curved cross-sections , 2008 .

[28]  Ben K. Wada,et al.  Adaptive structures - An overview , 1990 .

[29]  Maurizio Porfiri,et al.  Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation , 2004 .

[30]  Zhan Kang,et al.  Topology optimization of bending actuators with multilayer piezoelectric material , 2010 .

[31]  George A. Lesieutre,et al.  Can a Coupling Coefficient of a Piezoelectric Device be Higher Than Those of Its Active Material? , 1997, Smart Structures.

[32]  C. Maurinia,et al.  Numerical methods for modal analysis of stepped piezoelectric beams , 2006 .

[33]  Marcelo A. Trindade,et al.  Optimization of modal filters based on arrays of piezoelectric sensors , 2009 .

[34]  W. J. Karl,et al.  Cantilever unified theory and optimization for sensors and actuators , 2000 .

[35]  Raed I. Bourisli,et al.  Optimization of Smart Beams for Maximum Modal Electromechanical Coupling Using Genetic Algorithms , 2010 .

[36]  Quan Wang,et al.  Optimal placement and size of piezoelectric patches on beams from the controllability perspective , 2000 .

[37]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[38]  L. Gaul,et al.  Adaptive Structures-An Overview , 2005 .

[39]  José Carlos Bellido,et al.  TECHNICAL NOTE: Tailoring distributed modal sensors for in-plane modal filtering , 2009 .

[40]  Craig A. Rogers,et al.  Laminate Plate Theory for Spatially Distributed Induced Strain Actuators , 1991 .

[41]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[42]  Jean-François Deü,et al.  Structural Vibration Reduction by Switch Shunting of Piezoelectric Elements: Modeling and Optimization , 2010 .

[43]  J. Hollkamp.  Multimodal Passive Vibration Suppression with Piezoelectric Materials and Resonant Shunts , 1994 .

[44]  Byeng D. Youn,et al.  A design and experimental verification methodology for an energy harvester skin structure , 2011 .

[45]  Jean-François Deü,et al.  Optimization of Shunted Piezoelectric Patches for Vibration Reduction of Complex Structures: Application to a Turbojet Fan Blade , 2010 .

[46]  Francesco dell’Isola,et al.  A revival of electric analogs for vibrating mechanical systems aimed to their efficient control by PZT actuators , 2002 .

[47]  Eric B. Flynn,et al.  Optimal Placement of Piezoelectric Actuators and Sensors for Detecting Damage in Plate Structures , 2010 .

[48]  A. Chaigne,et al.  Asymmetric non-linear forced vibrations of free-edge circular plates. Part II: Experiments , 2003 .

[49]  Antonio Arnau,et al.  Fundamentals on Piezoelectricity , 2004 .

[50]  Cyril Touzé,et al.  ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY , 2002 .

[51]  Meng-Shiun Tsai,et al.  ON THE STRUCTURAL DAMPING CHARACTERISTICS OF ACTIVE PIEZOELECTRIC ACTUATORS WITH PASSIVE SHUNT , 1999 .

[52]  Manfred Morari,et al.  Adaptive multi-mode resonant piezoelectric shunt damping , 2004 .