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Suppressing Vibrations of a Rotating Active Composite Beam by a Cubic Velocity Feedback Control Method

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This study presents an analysis of a dynamic system consisting of a rigid hub and a cantilever flexible composite beam with an embedded active piezoelectric element. The system is excited by periodic oscillations of the hub angular speed. The macro fiber composite (MFC) active element is used to suppress beam vibrations. In the mathematical formulation of the problem the non-classical effects like material anisotropy and mode coupling due to an arbitrary stacking sequence of the laminate as well as the transverse shear deformations of the material are taken into account. Derived in previous research governing equations of the considered system are solved numerically by the finite difference method. Results of a numerical simulation are compared with experimental data including frequencies and mode shapes of natural vibrations and responses to unit step function excitations. Finally, the effectiveness of the piezoelectric actuator and the tested cubic velocity feedback control algorithm in order to suppress system vibrations is evaluated.
Opis fizyczny
Bibliogr. 16 poz., rys., wykr.
  • Lublin University of Technology, Department of Applied Mechanics
  • Lublin University of Technology, Department of Applied Mechanics
  • Lublin University of Technology, Department of Applied Mechanics
  • 1. Cai, G.-P., Hong, J.-Z., and Yang, S. X. (2004). Model study and active control of a rotating flexible cantilever beam. International Journal of Mechanical Sciences, 46(6):871–889.
  • 2. Choi, S.-C., Park, J.-S., and Kim, J.-H. (2006). Active damping of rotating composite thin-walled beams using MFC actuators and PVDF sensors. Composite Structures, 76(4):362–374.
  • 3. Gawryluk, J., Mitura, A., and Teter, A. (2016). Experimental and numerical studies on the static deflection of the composite beam with the MFC element. Mechanics and Mechanical Engineering, 20(2):97–108.
  • 4. Georgiades, F., Latalski, J., and Warminski, J. (2014). Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle. Meccanica, 49(8):1833–1858.
  • 5. Jun, L., Rongying, S., and Hongxing, H. (2007). Cubic velocity feedback control of high-amplitude vibration of a nonlinear plant to a primary resonance excitation. Shock and Vibration, 14(1):1–14.
  • 6. Latalski, J., Georgiades, F., and Warmiński, J. (2012). Rational placement of a macro fibre composite actuator in composite rotating beams. In Journal of Physics: Conference Series, volume 382, page 012021. IOP Publishing.
  • 7. Latalski, J. and Warmiński, J. (2015). Dynamics of a rotating thin-walled composite beam mounted on in plane moving hub. 3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics, 8-11 September 2015, Gdańsk, Poland, eds. M. Kleiber, T. Burczyński et al., 2:917–918.
  • 8. Latalski, J., Warmiński, J., and Rega, G. (2016). Bending–twisting vibrations of a rotating hub–thin-walled composite beam system. Mathematics and Mechanics of Solids, pages 1–23.
  • 9. Malatkar, P. (2003). Nonlinear vibrations of cantilever beams and plates. PhD thesis, Virginia Tech.
  • 10. Padoin, E., Fonseca, J. S. O., Perondi, E. A., and Menuzzi, O. (2015). Optimal placement of piezoelectric macro fiber composite patches on composite plates for vibration suppression. Latin American Journal of Solids and Structures, 12(5):925–947.
  • 11. Pietrzakowski, M. (2000). Multiple piezoelectronic segments in structural vibration control. Journal of Theoretical and Applied Mechanics, 38:35–50.
  • 12. Pietrzakowski, M. (2001). Experimental and analytical, investigation of actively damped beam vibrations. Mechanics and Mechanical Engineering, 5(2):111–120.
  • 13. Saaed, T. E., Nikolakopoulos, G., Jonasson, J.-E., and Hedlund, H. (2015). A state-of-the-art review of structural control systems. Journal of Vibration and Control, 21(5):919–937.
  • 14. Thomas, J. W. (2013). Numerical partial differential equations: finite difference methods, volume 22. Texts in Applied Mathematics, Springer Science & Business Media.
  • 15. Vadiraja, D. and Sahasrabudhe, A. (2009). Vibration analysis and optimal control of rotating pre-twisted thin-walled beams using MFC actuators and sensors. Thin-Walled Structures, 47(5):555–567.
  • 16. Warminski, J., Bochenski, M., Jarzyna, W., Filipek, P., and Augustyniak, M. (2011). Active suppression of nonlinear composite beam vibrations by selected control algorithms. Communications in Nonlinear Science and Numerical Simulation, 16(5):2237–2248.
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