Active modal control of vibrations in elastic structures in the presence of material damping. (English) Zbl 1116.74387
Summary: The current technology manifests a great demand for high precision and high positioning accuracy in many engineering applications that range from robot manipulators and high-speed flexible mechanisms to supercritical rotors and the space deployable structures. Active control is an important technique for suppressing vibrations in flexible mechanical systems where passive controllers may become either ineffective or impractical. A finite element model of the system dynamics in conjunction with modal reduction methods is introduced. The developed model accounts for the structural material damping. Pointwise observation and control are implemented using two sets of sensors and actuators, respectively. The developed computational active modal control algorithm is applied to the reduced order model of a double span elastic beam, and the dynamic responses of both the controlled and the residual frequency subsystems are numerically evaluated.
MSC:
| 74M05 | Control, switches and devices (“smart materials”) in solid mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
References:
| [1] | Crosby, M.; Karnopp, D., The active damper – a new concept for shock and vibration control, Shock Vib. Bull., 43, 4, 119-133 (1973) |
| [2] | M. Cotterel, Theoretical Analysis of an Active Suspension Fitted to a London Buss, in: Stress, Vibration and Noise Analysis in Vehicles, Halsted Press, New York, 1975, pp. 253-281; M. Cotterel, Theoretical Analysis of an Active Suspension Fitted to a London Buss, in: Stress, Vibration and Noise Analysis in Vehicles, Halsted Press, New York, 1975, pp. 253-281 |
| [3] | K. Seto, Trends on active vibration control in Japan, in: Proceedings of the First International Conference on Motion & Vibration Control, Yokohama, Japan, vol. 1, 1992, pp. 1-11; K. Seto, Trends on active vibration control in Japan, in: Proceedings of the First International Conference on Motion & Vibration Control, Yokohama, Japan, vol. 1, 1992, pp. 1-11 |
| [4] | Walker, L.; Yaneske, P., Characteristics of an active feedback system for the control of plate vibrations, J. Sound Vib., 46, 2, 157-176 (1976) · Zbl 0326.70016 |
| [5] | Nelson, P. A.; Elliott, S. J., Active Control of Sound (1992), Academic Press: Academic Press New York |
| [6] | Balas, M. J., Modal control of certain flexible dynamic systems, SIAM J. Control Optim., 16, 3, 450-462 (1978) · Zbl 0384.93036 |
| [7] | Balas, M. J., Feedback control of flexible systems, IEEE Trans. Autom. Control, AC-23, 4, 673-679 (1978) · Zbl 0381.93012 |
| [8] | Meirovitch, L.; Oz, H., Modal-space control of large flexible spacecraft possessing ignorable coordinates, J. Guidance Control, 3, 569-577 (1980) · Zbl 0471.93039 |
| [9] | C.R. Fuller, G.P. Gibbs, R.J. Silcox, Simultaneous active control of flexural and extensional power flow in beams, in: International Congress on Recent Developments in Air & Structure-Borne Sound & Vibration, Auburn University, AL, USA, March 1990, pp. 657-662; C.R. Fuller, G.P. Gibbs, R.J. Silcox, Simultaneous active control of flexural and extensional power flow in beams, in: International Congress on Recent Developments in Air & Structure-Borne Sound & Vibration, Auburn University, AL, USA, March 1990, pp. 657-662 |
| [10] | Clark, R. L.; Pan, J.; Hanson, C. H., An experimental study on the active control of multiple wave types in an elastic beam, J. Acoust. Soc. Am., 92, 2, 871-876 (1992) |
| [11] | Block, J. F.; Strganac, T. W., Active control for a nonlinear aeroleastic structure, AIAA J. Guidance, Control Dyn., 21, 6, 838-845 (1998) |
| [12] | Bernnan, M. J.; Day, M. J.; Randall, R. J., An experimental investigation into the semi-active and active control of longitudinal vibrations in large tie-rod structure, ASME J. Vib. Acoustics, 120, 1-12 (1998) |
| [13] | Skidmore, G. R.; Hallauer, W. L., Modal space active damping of a beam-cable structure: theory and experiment, J. Sound Vib., 101, 2, 149-160 (1985) |
| [14] | Khulief, Y. A.; Sun, S. P., Finite element modeling and semi-active control of vibrations in road vehicles, ASME J. Dyn. Syst., Meas. Control, 111, 521-527 (1989) · Zbl 0694.93071 |
| [15] | Lazan, B. J., Damping of Materials and Members in Structural Mechanics (1968), Pergamon Press: Pergamon Press Oxford |
| [16] | Sturla, F.; Argento, A., Free and forced vibrations of a spinning viscoelastic beam, ASME J. Vib. Acoustics, 118, 463-468 (1996) |
| [17] | Marsh, E. R.; Hale, L. C., Damping of flexural waves with imbeded viscoelastic materials, ASME J. Vib. Acoustics, 120, 188-193 (1998) |
| [18] | Likins, P. W., Modal methods for analysis of free rotations of spacecraft, AIAA J., 5, 7, 1304-1308 (1967) |
| [19] | Shabana, A. A.; Wehage, R., Variable degree of freedom component mode analysis of inertia variant flexible mechanical systems, ASME, J. Mech. Trans. Automat. Des., 105, 3, 370-378 (1983) |
| [20] | Spanos, T. J.; Tsuha, W. S., Selection of component modes for flexible multibody simulations, J. Guidance, 14, 2, 260-267 (1991) |
| [21] | Khulief, Y. A., On the finite element dynamic analysis of flexible mechanisms, J. Comput. Methods Appl. Mech. Engrg., 26, 41-55 (1997) · Zbl 0917.73068 |
| [22] | Meirovitch, L., A new method of solution of the eigenvalue problem for gyroscopic systems, AIAA J., 12, 10, 11337-11342 (1974) |
| [23] | Khulief, Y. A.; Mohiuddin, M. A., On the dynamics of rotors using modal reduction, J. Finite Elements Anal. Des., 97, 23 (1992) · Zbl 0917.73068 |
| [24] | Kwakernaak, H.; Sivan, R., Linear Optimal Control Systems (1972), Wiley: Wiley New York · Zbl 0276.93001 |
| [25] | Y.A. Khulief, Active control of vibrations in mechanically flexible systems, M.Sc. Thesis, The Hatfield Polytechnic, Hatfield, England, 1980; Y.A. Khulief, Active control of vibrations in mechanically flexible systems, M.Sc. Thesis, The Hatfield Polytechnic, Hatfield, England, 1980 |
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