Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach

Nonlinear vibrations of piezoelectric/elastic/piezoelectric sandwich beams submitted to active control are studied in this paper. The proportional and derivative potential feedback controls via sensor and actuator layers are used. Harmonic balance method and the Galerkin procedure are adopted. A complex amplitude equation governed by two complex parameters is derived accounting for the geometric nonlinearity and piezoelectric effects. The nonlinear frequency and loss-factor amplitude relationships with respect to the gain parameters are obtained. The feedback effects are analyzed for small and large vibration amplitudes of sandwich beams. The frequency response curves are presented and discussed for various gain parameters.

[1]  L. Azrar,et al.  SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF S–S AND C–C BEAMS AT LARGE VIBRATION AMPLITUDES PART I: GENERAL THEORY AND APPLICATION TO THE SINGLE MODE APPROACH TO FREE AND FORCED VIBRATION ANALYSIS , 1999 .

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

[3]  Ayech Benjeddou,et al.  Hybrid Active-Passive Damping Treatments Using Viscoelastic and Piezoelectric Materials: Review and Assessment , 2002 .

[4]  J. N. Reddy,et al.  On laminated composite plates with integrated sensors and actuators , 1999 .

[5]  Michel Potier-Ferry,et al.  Modélisation par éléments finis des vibrations non-linéaires des plaques sandwich viscoélastiques , 2005 .

[6]  Satya N. Atluri,et al.  Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading , 1989 .

[7]  R. Benamar,et al.  AN ASYMPTOTIC-NUMERICAL METHOD FOR LARGE-AMPLITUDE FREE VIBRATIONS OF THIN ELASTIC PLATES , 1999 .

[8]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[9]  H. Abramovich,et al.  Induced vibrations of piezolaminated elastic beams , 1998 .

[10]  Michel Potier-Ferry,et al.  Modal approach to evaluate passive and active damping of sandwich viscoelastic and piezoelectric beams , 2004 .

[11]  Jx X. Gao,et al.  Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators , 2003 .

[12]  Carlos A. Mota Soares,et al.  Geometrically non-linear analysis of composite structures with integrated piezoelectric sensors and actuators , 2002 .

[13]  Michel Potier-Ferry,et al.  An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams , 2004 .

[14]  Roger Ohayon,et al.  A Unified Beam Finite Element Model for Extension and Shear Piezoelectric Actuation Mechanisms , 1997 .

[15]  R. Benamar,et al.  a Semi-Analytical Approach to the Non-Linear Dynamic Response Problem of Beams at Large Vibration Amplitudes, Part II: Multimode Approach to the Steady State Forced Periodic Response , 2002 .

[16]  Inderjit Chopra,et al.  Structural modeling of composite beams with induced-strain actuators , 1993 .

[17]  Laëtitia Duigou-Kersulec.  Modélisation numérique de l'amortissement passif et actif des tôles sandwich comportant des couches viscoélastiques ou piézoélectriques , 2002 .