FEM Analysis of Active Reduction of Torsional Vibrations of Clamped-Free Beam by Piezoelectric Elements for Separated Modes
Abstract
Beams with rectangular cross-section, with large length-to-width ratio, can be excited to torsional vibrations. If the piezoelectric elements are mounted to the beam in pairs at the same cross-section with two separated elements positioned on the same side of the beam, and the voltages applied to them are in the opposite phase, they produce twisting moments which can be applied to reduce the torsional vibrations. Results of FEM simulations are presented and analysed in the paper. All analyses are performed for a steel free-clamped beam. The piezoelectric elements made of PZT material are mounted in pairs on one side of the beam. The analyses are done for separated natural modes.Keywords:
piezoelectric elements, torsional vibrations.References
Augustyn E., Kozień M.S. (2014). A Study on Possibility to Apply piezoelectric Actuators for Active Reduction of Torsional Beams Vibration, Acta Physica Polonica A, 125(4-A), 164-168.
Brański A., Szela S. (2010). Quasi-optimal PZT distribution in active vibration reduction of the triangular plate with P-F-F boundary conditions. Archives of Control Sciences, 20(LVI) (2), 209-226.
Brański A., Lipiński G. (2011). Analytical Determination of the PZT's Distribution in Active Beam Vibration. Acta Physica Polonica A, 119, 936-941.
Filipek R., Wiciak J. (2008). Active and passive structural acoustic control of the smart beam. European Physical Journal , 154, 57-63.
Gryboś R. (1996). Vibrations of machines (in Polish). Politechnika Śląska, Gliwice.
Hohl A., Neubauer M., Schwarzendahl S.M., Panning L., Wallaschek J. (1996). Active and semiactive vibration damping of turbine blades with piezoceramics. Proceedings of SPIE, 7288.
Kozień M.S., Wiciak J. (2009). Choosing of optimal voltage amplitude of four pairs square piezoelectric elements for minimization of acoustic radiation of vibrating plate. Acta Physica Polonica A, 116, 348-350.
Łączkowski R. (1974). Vibrations of elements of turbine machines (in Polish). WNT, Warszawa.
Rao J.S. (1991). Turbomachine Blade Vibration, Wiley, Chichester.
Pust L., Pesek L. (2014). Blade couple connected by damping element with dry friction. Journal of Theoretical and Applied Mechanics, 52.
Shoushtari N.D. (1964). Optimal Active Control of Flexible Structures Applying Piezoelectric Actuators. PhD Thesis, California Institute of Technology, Pasadena, California.
Straub T., Kennerknecht T., Robin P., Tort M., Kieffer G., Lapusta Y., Eberl C. (2011). Small-scale multiaxial fatigue experiments in the very high cycle regime. Proceedings of the 5th International Conference on Very High Cycle Fatigue (Eds.: Berger C., Christ H.-J.), Berlin, 473-478.
Wiciak J., Trojanowski R. (2014). The effect of material composition of piezoelectric elements with chosen shapes on plate vibration reduction. Acta Physica Polonica A, 125(4-A), 179-182.
Wiciak M., Trojanowski R.. (2014). Numerical analysis of the effectiveness of two-part piezoactuators in vibration reduction of plates. Acta Physica Polonica A, 125(4-A), 183-189.
Żołopa E., Brański A. (2014). Analytical determination of optimal actuators position for single mode active reduction of fixed-free beam vibration using the linear quadratic problem idea. Acta Physica Polonica A, 125(4-A), 155-158.
Brański A., Szela S. (2010). Quasi-optimal PZT distribution in active vibration reduction of the triangular plate with P-F-F boundary conditions. Archives of Control Sciences, 20(LVI) (2), 209-226.
Brański A., Lipiński G. (2011). Analytical Determination of the PZT's Distribution in Active Beam Vibration. Acta Physica Polonica A, 119, 936-941.
Filipek R., Wiciak J. (2008). Active and passive structural acoustic control of the smart beam. European Physical Journal , 154, 57-63.
Gryboś R. (1996). Vibrations of machines (in Polish). Politechnika Śląska, Gliwice.
Hohl A., Neubauer M., Schwarzendahl S.M., Panning L., Wallaschek J. (1996). Active and semiactive vibration damping of turbine blades with piezoceramics. Proceedings of SPIE, 7288.
Kozień M.S., Wiciak J. (2009). Choosing of optimal voltage amplitude of four pairs square piezoelectric elements for minimization of acoustic radiation of vibrating plate. Acta Physica Polonica A, 116, 348-350.
Łączkowski R. (1974). Vibrations of elements of turbine machines (in Polish). WNT, Warszawa.
Rao J.S. (1991). Turbomachine Blade Vibration, Wiley, Chichester.
Pust L., Pesek L. (2014). Blade couple connected by damping element with dry friction. Journal of Theoretical and Applied Mechanics, 52.
Shoushtari N.D. (1964). Optimal Active Control of Flexible Structures Applying Piezoelectric Actuators. PhD Thesis, California Institute of Technology, Pasadena, California.
Straub T., Kennerknecht T., Robin P., Tort M., Kieffer G., Lapusta Y., Eberl C. (2011). Small-scale multiaxial fatigue experiments in the very high cycle regime. Proceedings of the 5th International Conference on Very High Cycle Fatigue (Eds.: Berger C., Christ H.-J.), Berlin, 473-478.
Wiciak J., Trojanowski R. (2014). The effect of material composition of piezoelectric elements with chosen shapes on plate vibration reduction. Acta Physica Polonica A, 125(4-A), 179-182.
Wiciak M., Trojanowski R.. (2014). Numerical analysis of the effectiveness of two-part piezoactuators in vibration reduction of plates. Acta Physica Polonica A, 125(4-A), 183-189.
Żołopa E., Brański A. (2014). Analytical determination of optimal actuators position for single mode active reduction of fixed-free beam vibration using the linear quadratic problem idea. Acta Physica Polonica A, 125(4-A), 155-158.
