Active damping of geometrically nonlinear transverse beam vibrations

• Autorzy: Tylikowski, A.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with the stabilization of an elastic beam nonlinear geometrically subjected to a time-dependent axial forcing. The direct Liapunov method is proposed to establish criteria for the almost sure stochastic stability of the unperturbed (trivial) solution of the structure with closed-loop control. We construct the Liapunov functional as a sum of the modified kinetic energy and the elastic energy of the structure The distributed control is realized by the piezoelectric sensor and actuator, with the changing widths, glued to the upper and lower beam surface. The paper is devoted to the stability analysis of the closed-loop system described by the stochastic partial differential equation without a finite-dimensional approach. The fluctuating axial force is modelled by the physically realizable ergodic process. The rate velocity feedback is applied to stabilize the panel parametric vibrations. Calculations are performed for the Gaussian process with given mean value and variance as well as for the harmonic process with an amplitude A.

Słowa kluczowe

PL

tłumienie aktywne; belka poprzeczna; sterowanie piezoelektryczne

EN

active damping; transverse beam; piezoelectric control

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2001
• Tom: Vol. 5, nr 2
• Strony: 127-135
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Tylikowski, A.

• Warsaw University of Technology, Narbutta 84,02-524 Warszawa, Poland

Bibliografia

• 1. CRAWLEY E. F., and de LUIS J., 1987, Use of piezoelectric actuators as elements of intelligent structures, AIAAL, 25, 1373-1385.
• 2. DIMITRIDIS E., FULLER C. E., and ROGERS C. A., 1991, Piezoelectric actuators for distributed vibration excitation of thin plates, J. Appl. Mech., 113, 100-107.
• 3. KOZIN F., 1972, Stability of the linear stochastic system, Lecture Notes in Mathematics, 294, 186-229.
• 4. TYLIKOWSKI A., 1994, Dynamics of laminated beam with active fibers, Proceedings of the 3-rd Polish- German Workshop on Dynamical Problems in Mechanical Systems, R. Bogacz, and K. Popp, (eds.), Wierzba, IPPT PAN, 67-78.
• 5. TYLIKOWSKI A., 1995, Active stabilization of beam vibrations parametrically excited by wide- band Gaussian force, Proceedings of The International Symposium on Active Control of Sound and Vibration, S. D. Sommerfelt, and H. Hamada (eds.), Technomic Publishing, Lancaster-Basel, 91-102 .
• 6. TYLIKOWSKI, A., Stabilization of beam parametric vibrations by means of distributed piezoelectric elements, J. Theoret. Appl. Mech., 37,1999, 241-254.
• 7. TZOU H. S. , and FU H. Q., 1992, A study on segmentation of distributed piezoelectric sensors and actuators; Part 1 - Theoretical analysis, Active Control of Noise and Vibration, ASME, DSC - 38, 239-46.