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.

Simulation of Control Algorithm for Active Reduction of Transversal Vibrations of Beams by Piezoelectric Elements Based on Identification of Bending Moment

“…equivalent bending moment M eq can be written in the form (5), where E p is the Young modulus of the piezoelectric material, h and h p are thicknesses of the beam and the piezoelectric element, respectively, and d zx is the charge constant of the piezoelectric material [10]. Hence, the value of the equivalent bending moment depends on the type of the materials that the beam and the attached element are made out of, the thickness of the beam, as well as on thickness of the element and the applied voltage.…”

“…2. The actuating voltage under a control algorithm can be determined based on formula (5). It produces the antibending moment for reducing the vibration of the system (6).…”

“…Reduction of bending vibrations of beams by piezoelectric elements is a well-known idea. Such reduction can be realized in a passive or active form for different types of the beam response (unimodal, bimodal, or multimodal) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

“…The general rule provides for placing the elements in areas where the bending moment has maximum values [7,19,20]. This idea was applied in [4,5] to simulation of reduction of torsional vibrations of the beam.…”

Comparison of Formulas Obtained for Analytical and LQ Idea Approaches to Determine the Optimal Actuator Location in Active Multimodal Beam Vibration Reduction

“…There are also many structures of which the vibrations are reduced via actuators, from the simple beam (Augustyn et al, 2014;Brański, 2011), through the plate (Wiciak, 2007) to the very complicated structure (Kozień, Wiciak, 2008).…”