@ARTICLE{Augustyn_Elżbieta_FEM_2014, author={Augustyn, Elżbieta and Kozień, Marek S. and Pracik, Michał}, volume={vol. 39}, number={No 4}, journal={Archives of Acoustics}, pages={639-644}, howpublished={online}, year={2014}, publisher={Polish Academy of Sciences, Institute of Fundamental Technological Research, Committee on Acoustics}, 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.}, type={Artykuły / Articles}, title={FEM Analysis of Active Reduction of Torsional Vibrations of Clamped-Free Beam by Piezoelectric Elements for Separated Modes}, URL={http://www.czasopisma.pan.pl/Content/101492/PDF/23_paper.pdf}, doi={10.2478/aoa-2014-0069}, keywords={piezoelectric elements, torsional vibrations}, }