Multimodal vibration damping through a periodic array of piezoelectric patches connected to a passive network

In damping devices involving piezoelectric elements, a single piezoelectric patch cannot consistently achieve multimodal control because of charge cancellation or vibration node location. In order to sense and control structural vibration on a prescribed frequency range, a solution consists in using an array of several piezoelectric patches being small compared to the smallest wavelength to control. Then, as an extension of the tuned mass damper strategy, a passive multimodal control requires to implement a damping system whose modes are as close as possible to those of the controlled structure. In this way, the electrical equivalent of the discretized mechanical structure represents the passive network that optimizes the energy transfer between the two media. For one-dimensional structures, a periodic distribution in several unit cells enables the use of the transfer matrix method applied on electromechanical state-vectors. The optimal passive networks are obtained for the propagation of longitudinal and transverse waves and a numerical implementation of the coupled behavior is performed. Compared to the more classical resonant shunts, the network topology induces promising multimodal damping and a reduction of the needed inductance. It is thus possible to create a completely passive electrical structure as it is demonstrated experimentally by using only purely passive components.

[1]  S. Vidoli,et al.  Modal coupling in one-dimensional electromechanical structured continua , 2000 .

[2]  A. Bloch,et al.  Electromechanical analogies and their use for the analysis of mechanical and electromechanical systems , 1945 .

[3]  Francesco dell’Isola,et al.  Extension of the Euler-Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach , 2006 .

[4]  Giovanni Caruso,et al.  Optimized electric networks for vibration damping of piezoactuated beams , 2006 .

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

[6]  Jiong Tang,et al.  Electromechanical tailoring of structure with periodic piezoelectric circuitry , 2012 .

[7]  F.dell'Isola,et al.  Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation , 2010 .

[8]  Jihong Wen,et al.  Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits , 2011 .

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

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

[11]  Boris Lossouarn,et al.  Multimodal coupling of periodic lattices and application to rod vibration damping with a piezoelectric network , 2015 .

[12]  Maurizio Porfiri,et al.  Piezoelectric Passive Distributed Controllers for Beam Flexural Vibrations , 2004 .

[13]  W. Marsden I and J , 2012 .

[14]  Massimo Ruzzene,et al.  Wave Propagation Control in Beams Through Periodic Multi-Branch Shunts , 2011 .

[15]  Massimo Ruzzene,et al.  Experimental Analysis of a Cantilever Beam with a Shunted Piezoelectric Periodic Array , 2011 .

[16]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

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

[18]  Jihong Wen,et al.  Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou’s circuit: experimental investigation on beams , 2010 .

[19]  Manuel Collet,et al.  Experimental assessment of negative impedance shunts for vibration suppression on a beam , 2008, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

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

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

[22]  A. P,et al.  Mechanical Vibrations , 1948, Nature.

[23]  L. Brillouin,et al.  Wave Propagation in Periodic Structures , 1946 .

[24]  D. M. Mead,et al.  WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES: RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON, 1964–1995 , 1996 .