The performance of pulse-switching vibration control technique is investigated using a new method for switching sequence, in order to enhance the vibration damping. The control law in this method which was developed in the field of piezoelectric damping is based on triggering the inverting switch on each extremum of the produced voltage (or displacement); however, its efficiency in the case of random excitation is arguable because of the local extremum detection process. The new proposed method for switching sequence is only based on the fact that the triggering voltage level was determined using windowed statistical examination of the deflection signal. Results for a cantilever beam excited by different excitation forces, such as stationary and nonstationary random samples, and pulse forces are presented. A significant decrease in vibration energy and also the robustness of this method are demonstrated. 1. Introduction The ability to reduce the vibration amplitude over a wide frequency band is essential in the vibration control. The dependency of dynamic stiffness and damping properties of special materials such as viscoelastic materials on the excitation frequency or temperature variations cause other methods or materials to be considered [1, 2]. Several methods have been investigated for semi-active vibration control, using piezoelectric elements [3–10]. These methods are interesting because they do not rely on any operating energy as in active control. They consist of driving by a few solid-state switches requiring very little power. The common strategy of these methods is the electric boundary conditions modification of the piezoelectric elements. Synchronized Switch Damping (SSD) or pulse-switching technique which is implemented in this study consists of leaving the piezoelectric elements in open circuit, except during a very brief period of time, where the electric charge is either suppressed in a short circuit (SSDS) or inverted with a resonant network (SSDI). Corr and Clark experimented with SSDI method in the case of multimodal vibrations [5]. Also, they showed that the original SSD control law is not optimal in the case of wide band excitations. In the case of wide band excitations, the optimization of the piezoelectric elements (size and location) as well as the switching network is not sufficient. It is therefore necessary to establish methods to define the accurate switch triggering time that operates exclusively on certain selected extrema, which would maximize the electric power produced by the piezoelectric elements [3]. In a similar
References
[1]
A. L. Webster and W. H. Semke, “Broad-band viscoelastic rotational vibration control for remote sensing applications,” Journal of Vibration and Control, vol. 11, no. 11, pp. 1339–1356, 2005.
[2]
M. D. Rao, “Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes,” Journal of Sound and Vibration, vol. 262, no. 3, pp. 457–474, 2003.
[3]
D. Guyomar, C. Richard, and S. Mohammadi, “Semi-passive random vibration control based on statistics,” Journal of Sound and Vibration, vol. 307, no. 3–5, pp. 818–833, 2007.
[4]
A. Badel, G. Sebald, D. Guyomar et al., “Piezoelectric vibration control by synchronized switching on adaptive voltage sources: towards wideband semi-active damping,” Journal of the Acoustical Society of America, vol. 119, no. 5, pp. 2815–2825, 2006.
[5]
L. R. Corr and W. W. Clark, “A novel semi-active multi-modal vibration control law for a piezoceramic actuator,” Journal of Vibration and Acoustics, vol. 125, no. 2, pp. 214–222, 2003.
[6]
D. Guyomar and A. Badel, “Nonlinear semi-passive multimodal vibration damping: an efficient probabilistic approach,” Journal of Sound and Vibration, vol. 294, no. 1-2, pp. 249–268, 2006.
[7]
W. Q. Liu, Z. H. Feng, J. He, and R. B. Liu, “Maximum mechanical energy harvesting strategy for a piezoelement,” Smart Materials and Structures, vol. 16, no. 6, pp. 2130–2136, 2007.
[8]
H. Ji, J. Qiu, K. Zhu, Y. Chen, and A. Badel, “Multi-modal vibration control using a synchronized switch based on a displacement switching threshold,” Smart Materials and Structures, vol. 18, no. 3, Article ID 035016, 8 pages, 2009.
[9]
H. Ji, J. Qiu, K. Zhu, and A. Badel, “Two-mode vibration control of a beam using nonlinear synchronized switching damping based on the maximization of converted energy,” Journal of Sound and Vibration, vol. 329, no. 14, pp. 2751–2767, 2010.
[10]
H. Ji, J. Qiu, and P. Xia, “Analysis of energy conversion in two-mode vibration control using synchronized switch damping approach,” Journal of Sound and Vibration, vol. 330, no. 15, pp. 3539–3560, 2011.
[11]
A. Steinwolf, N. S. Ferguson, and R. G. White, “Variations in steepness of the probability density function of beam random vibration,” European Journal of Mechanics A, vol. 19, no. 2, pp. 319–341, 2000.
[12]
L. D. Lutes and S. J. Hu, “Non-normal stochastic response of linear system,” Journal of Engineering Mechanics (ASCE), vol. 112, no. 2, pp. 127–141, 1986.
[13]
C. G. Bucher and G. I. Schueller, “Non-Gaussian response of linear systems,” in Structural Dynamics. Recent Advances, pp. 103–127, Springer, Berlin, Germany, 1991.
[14]
J. B. Roberts, “On the response of a simple oscillator to random impulses,” Journal of Sound and Vibration, vol. 4, no. 1, pp. 51–61, 1966.
[15]
K. G. McConnell, Vibration Testing Theory and Practice, John Wiley & Sons, New York, NY, USA, 1995.
[16]
D. Steinberg, Vibration Analysis for Electronic Equipment, Wiley-Interscience, New York, NY, USA, 1988.
[17]
W. T. Thomson, Theory of Vibration With Applications, Prentice-Hall, Englewood Cliffs, NJ, USA, 1981.
[18]
M. Sakata and K. Kimura, “Calculation of the non-stationary mean square response of a non-linear system subjected to non-white excitation,” Journal of Sound and Vibration, vol. 73, no. 3, pp. 333–343, 1980.
