AN EFFICIENT FINITE ELEMENT APPROACH FOR REDUCTION OF STRUC- TURAL VIBRATION AND ACOUSTIC RADIATION BY PASSIVE SHUNTED PIE- ZOELECTRIC SYSTEMS

The present work concerns the numerical modeling of noise and vibration reduc- tion of thin radiating structures in the low frequency range by using shunted piezoelectric elements. The aim is to propose an efficient approach able to predict the structures most ra- diating vibration modes and to attenuate these modes by using piezoelectric patches bonded on the structure and connected to resistive or resonant shunt. The first step is to estimate the sound power radiated by the structure and determine the vibration modes to be controlled. In a second step, an original finite element formulation, adapted to any elastic structures with surface-mounted piezoelectric patches, is proposed to solve the electromechanical problem. Finally, numerical examples are presented in order to validate and analyze our approach. The use of piezoelectric materials for vibration damping and noise suppression of flex- ible structures, both in active control (3, 6, 9, 21) and in passive control (4, 7-8, 12-13, 15-24), is widely discussed in the literature. These materials, which can be used as sensors or actua- tors, or even both simultaneously, enable the transformation of mechanical energy into elec- tric energy (direct piezoelectric effect) and vice-versa (indirect piezoelectric effect). Also, they are well adapted to distributed or localized control of structural vibrations and sound radiation since they are produced as very thin patches that can be embedded in composite structure and allow direct connection with an input/output electrical signal (23). Due to the direct piezoelectric effect, a portion of the mechanical energy associated with the vibration can be transformed into electric energy and dissipated through a shunt cir- cuit that compounds a mechanism of passive damping. A detailed description of the use of shunt circuit and piezoelectric devices can be found in the pioneer work of Hagood and von Flotow (12). In that work, the expression for the mechanical impedance introduced by the

[1]  Francesco dell’Isola,et al.  Control of sound radiation and transmission by a piezoelectric plate with an optimized resistive electrode , 2010 .

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

[3]  Amâncio Fernandes,et al.  Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results , 2001 .

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

[5]  Roger Ohayon,et al.  Structural-Acoustic Vibration Reduction Using Switched Shunt Piezoelectric Patches: A Finite Element Analysis , 2010 .

[6]  André Preumont,et al.  Contrôle actif du rayonnement acoustique des plaques: une approche à faible autorité , 2004 .

[7]  C. Wallace Radiation Resistance of a Rectangular Panel , 1972 .

[8]  Marcelo A. Trindade,et al.  Multimodal passive vibration control of sandwich beams with shunted shear piezoelectric materials , 2008 .

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

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

[11]  V. Steffen,et al.  Multimodal vibration damping through piezoelectric patches and optimal resonant shunt circuits , 2006 .

[12]  Jean-François Deü,et al.  Placement and dimension optimization of shunted piezoelectric patches for vibration reduction , 2012 .

[13]  Roger Ohayon,et al.  Piezoelectric structural acoustic problems: Symmetric variational formulations and finite element results , 2008 .

[14]  Berkhoff Sensor scheme design for active structural acoustic control , 2000, The Journal of the Acoustical Society of America.

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

[16]  Kenneth A. Cunefare,et al.  Modal Synthesis and Dynamical Condensation Methods for Accurate Piezoelectric Systems Impedance Computation , 2008 .

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

[18]  Roger Ohayon,et al.  Finite element modelling of hybrid active–passive vibration damping of multilayer piezoelectric sandwich beams—part I: Formulation , 2001 .

[19]  S. Elliott,et al.  Radiation modes and the active control of sound power , 1993 .

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

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

[22]  Ayech Benjeddou,et al.  Advances in piezoelectric finite element modeling of adaptive structural elements: a survey , 2000 .