Free Vibrations Stability Analysis and Control of a Cantilever beam with Multiple Time Delay State Feedback

gures showing the stability regions as a function of the controller gains and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct longtime integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated, and compared. To validate the single mode approximation, numerical simulations are performed using three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the rst-mode vibration.

[1]  Abdollah Homaifar,et al.  Genetic algorithms and fuzzy-based vibration control of plate using PZT actuators , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[2]  J. F. Ribeiro,et al.  Experiments on Optimal Vibration Control of a Flexible Beam Containing Piezoelectric Sensors and Actuators , 2003 .

[3]  M. R. Silva,et al.  Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion , 1978 .

[4]  Mansour Karkoub,et al.  Active, Shunted, and Passive Constrained Layer Damping for the Vibration Suppression of a Flexible Four-Bar Mechanism , 2001 .

[5]  R. Skelton,et al.  Component cost analysis of large scale systems , 1983 .

[6]  M. R. Silva,et al.  Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. II. Forced Motions , 1978 .

[7]  Martin Hosek,et al.  A TUNABLE TORSIONAL VIBRATION ABSORBER: THE CENTRIFUGAL DELAYED RESONATOR , 1997 .

[8]  Damir Filipović,et al.  Delayed resonator with speed feedback – design and performance analysis , 2002 .

[9]  George A. Lesieutre,et al.  Vibration damping and control using shunted piezoelectric materials , 1998 .

[10]  Ziyad N. Masoud,et al.  Nonlinear free vibration control of beams using acceleration delayed-feedback control , 2008 .

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

[12]  Ali H. Nayfeh,et al.  Sway Reduction on Container Cranes Using Delayed Feedback Controller , 2003 .

[13]  Nejat Olgac,et al.  A Novel Active Vibration Absorption Technique: Delayed Resonator , 1994 .

[14]  Abdollah Homaifar,et al.  Active control of flexible structure using genetic algorithms and LQG/LTR approaches , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[15]  Ali H. Nayfeh,et al.  Cargo Pendulation Reduction of Ship-Mounted Cranes , 2004 .

[16]  Jon R. Pratt,et al.  A Nonlinear Vibration Absorber for Flexible Structures , 1998 .

[17]  C. I. Tseng,et al.  Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach , 1990 .

[18]  D. K. Rao,et al.  Frequency and Loss Factors of Sandwich Beams under Various Boundary Conditions , 1978 .

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

[20]  Nader Jalili,et al.  MULTIPLE DELAYED RESONATOR VIBRATION ABSORBERS FOR MULTI-DEGREE-OF-FREEDOM MECHANICAL STRUCTURES , 1999 .

[21]  Suhuan Chen,et al.  Integrated structural and control optimization of intelligent structures , 1999 .

[22]  D. J. Mead,et al.  The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions , 1969 .

[23]  Martin Hosek,et al.  Active Vibration Control of Distributed Systems Using Delayed Resonator With Acceleration Feedback , 1997 .

[24]  A. Nayfeh,et al.  On the Transfer of Energy between Widely Spaced Modes in Structures , 2003 .

[25]  Nader Jalili,et al.  MODAL ANALYSIS OF FLEXIBLE BEAMS WITH DELAYED RESONATOR VIBRATION ABSORBER: THEORY AND EXPERIMENTS , 1998 .

[26]  Conor D. Johnson,et al.  Finite Element Prediction of Damping in Structures with Constrained Viscoelastic Layers , 1981 .

[27]  Ali H. Nayfeh,et al.  A Parametric Identification Technique for Single-Degree-of-Freedom Weakly Nonlinear Systems with Cubic Nonlinearities , 2003 .