Archives of Acoustics, 39, 4, pp. 605-613, 2014
10.2478/aoa-2014-0065

Control of Bending-Bending Coupled Vibrations of a Rotating Thin-Walled Composite Beam

Jaroslaw LATALSKI
Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin
Poland

Marcin BOCHEŃSKI
Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin
Poland

Jerzy WARMIŃSKI
Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin
Poland

The paper presents a study of a possible application of structure embedded piezoelectric actuators to enhance the performance of a rotating composite beam exhibiting the coupled flexural-flexural vibrations. The discussed transversal and lateral bending modal coupling results from the directional properties of the beam’s laminate and ply stacking distribution. The mathematical model of the beam is based on an assumption of cross-sectional non-deformability and it incorporates a number of non-classical effects. The final 1-D governing equations of an active composite beam include both orthotropic properties of the laminate and transversely isotropic properties of piezoelectric layers. The system’s control capabilities resulting from embedded Macro Fiber Composite piezoelectric actuators are represented by the boundary bending moment. To enhance the dynamic properties of the composite specimen under consideration a combination of linear proportional control strategies has been used. Comparison studies have been performed, including the impact on modal coupling magnitude and cross-over frequency shift.
Keywords: thin-walled beam, adaptive materials, feedback control, composite beam, coupled vibrations, structural tailoring.
Full Text: PDF

References

Baruh, H. (1999), Analytical dynamics, WCB/McGraw-Hill, Singapore.

Birman, V. (1994), ‘Analytical models of sandwich plates with piezoelectric strip-stiffeners’, International Journal of Mechanical Sciences 36(6), 567–578.

Georgiades, F., Latalski, J. & Warminski, J. (2014), ‘Equations of motion of rotating composite beams with a nonconstant rotation speed and an arbitrary preset angle’, Meccanica 49(8), 1833–1858.

Hodges, D. H. (2006), Nonlinear composite beam theory, Vol. 213 of Progress in astronautics and aeronautics, American Institute of Aeronautics and Astronautics.

Housner, G. W., Bergman, L. A., Caughey, T. K., Chassiakos, A. G., Claus, R. O., Masri,

S. F., Skelton, R. E., Soong, T. T., Spencer, B. F. & Yao, J. T. P. (1997), ‘Structural control: Past, present, and future’, Journal of Engineering Mechanics 123(9), 897–971.

Kovvali, R. K. & Hodges, D. H. (2012), ‘Verification of the variational-asymptotic sectional analysis for initially curved and twisted beams’, Journal of Aircraft 49(3), 861–869.

Lagnese, J. (1989), Boundary Stabilization of Thin Plates, SIAM Studies in Applied Mechanics, SIAM, Philadelphia.

Latalski, J., Bochenski, M., Warminski, J., Jarzyna, W. & Augustyniak, M. (2014), ‘Modelling and simulation of 3 blade helicopter’s rotor model’, Acta Physica Polonica A 125(4), 1380–1384.

Latalski, J., Georgiades, F. & Warminski, J. (2012), ‘Rational placement of a macro fibre composite actuator in composite rotating beams’, Journal of Physics: Conference Series

(1), 012021.

Leissa, A. & Co, C. (1984), Coriolis effects on the vibration of rotating beams and plates, in ‘Proceedings of the 12th Southeastern Conference on Theoretical and Applied Mechanics’, Pine Mountain (GA), USA, pp. 508–513.

Librescu, L., Meirovitch, L. & Na, S. (1997), ‘Control of cantilever vibration via structural tailoring and adaptive materials’, AIAA Journal 35(8), 1309–1315.

Librescu, L. & Na, S. (1998), ‘Dynamic response control of thin-walled beams to blast pulses using structural tailoring and piezoelectric actuation’, Journal of Applied Mechanics

(2), 497–504.

Librescu, L. & Song, O. (2006), Thin-Walled Composite Beams, Springer.

Librescu, L., Song, O. & Rogers, C. (1993), ‘Adaptive vibrational behavior of cantilevered structures modeled as composite thin-walled beams’, International Journal of Engineering Science 31(5), 775–792.

Mesecke-Rischmann, S. (2004), Modellierung von flachen piezoelektrischen schalen mit zeverlassigen finiten elementen, Master’s thesis, Institute fur Mechanik, Universitat der Bundeswehr, Hamburg.

Piefort, V. (2001), Finite element modelling of piezoelectric active structures, Master’s thesis, Faculty of Applied Sciences, Universit´e Libre de Bruxelles.

Rao, S. S. & Sunar, M. (1994), ‘Piezoelectricity and its use in disturbance sensing and control of flexible structures: A survey’, Applied Mechanics Reviews 47(4), 113–123.

Rehfield, L. W., Atilgan, A. R. & Hodges, D. H. (1990), ‘Nonclassical behavior of thin-walled composite beams with closed cross sections’, Journal of the American Helicopter Society 35(2), 42–50.

Shabana, A. (2005), Dynamics of multibody systems, Cambridge University Press.

Song, O., Kim, J.-B. & Librescu, L. (2001), ‘Synergistic implications of tailoring and adaptive materials technology on vibration control of anisotropic thin-walled beams’, International Journal of Engineering Science 39(1), 79–94.

Song, O. & Librescu, L. (1993), ‘Free vibration of anisotropic composite wthin-walled beams of closed cross-section contour’, Journal of Sound and Vibration 167(1), 129–147.

Song, O. & Librescu, L. (1996), ‘Bending vibrations of adaptive cantilevers with external stores’, International Journal of Mechanical Sciences 38(5), 483–498.

Song, O. & Librescu, L. (1997), ‘Structural modeling and free vibration analysis of rotating composite thin-walled beams’, Journal of The American Helicopter Society 42(4), 358–369.

Sunar, M. & Rao, S. S. (1999), ‘Recent advances in sensing and control of flexible structures via piezoelectric materials technology’, Applied Mechanics Reviews 52(1), 1–16.

Tzou, H. S. & Zhong, J. P. (1992), Adaptive piezoelectric structures: Theory and experiment, in G. Knowels, ed., ‘Active Materials and Adaptive Structures - Proceedings of the Proceedings of the ADPA/AIAA/ASME/SPIE Conference’, Smart Materials and Structures Series, Institute of Physics, Alexandria (VA), USA, pp. 719–724.

Warminski, J., Bochenski, M., Jarzyna, W., Filipek, P. & 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.

Yu, W., Hodges, D. H., Volovoi, V. V. & Fuchs, E. D. (2005), ‘A generalized Vlasov theory for composite beams’, Thin-Walled Structures 43(9), 1493–1511.




DOI: 10.2478/aoa-2014-0065

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN)