Stability of rotating shafts in a weak formulation

• Autorzy: Tylikowski A.
• Konferencja: Symposium Vibrations In Physical Systems (23 ; 28-31.05.2008 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The stability analysis method is developed for a thin-walled rotating shaft with relaxed assumptions imposed on solutions. The problem is motivated by structural vibrations with external time-dependent parametric excitations which are controlled using surface mounted or embedded actuators and sensors. The commonly used strong form of dynamics equations involves irregularities which lead to computational difficulties for estimation and control problems. In order to avoid irregular terms resulting from differentiation of torques the dynamics equations are written in a weak form. The study of stability analysis is based on examining properties of Liapunov functional along a weak solution. Solving the problem is presented for an arbitrary combination of simply supported and clamped boundary conditions. Formulas defining dynamic stability regions are written explicitly.

Słowa kluczowe

EN

weak form; thin-walled shaft; dynamic stability; different boundary conditions

PL

forma słaba; wał cienkościenny; stateczność dynamiczna; graniczne warunki brzegowe

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2008
• Tom: Vol. 23
• Strony: 377--382
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Tylikowski A.

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

Bibliografia

• 1. H. T. Banks, W. Fang, R. J. Silcox, R. C. Smith, Approximation methods for control of structural acoustics models with piezoelectric actuators, Journal of Intelligent Material Systems and Structures, 4 (1993) 98-116.
• 2. O. A. Bauchau, Optimal design of high speed rotating graphite/epoxy shafts, J. Composite Materials, 17 (1983)170 -181.
• 3. K. F. Graff, Wave motion in elastic solids, Dover Publications, New York, 1975.
• 4. R. Pavlović, P. Rajković, I. Pavlović, Dynamic stability of the viscoelastic rotating shaft subjected to random excitation, Intern. J. Mechanical Sciences 50 (2008) 359-364.
• 5. A. Tylikowski, Dynamic stability of rotating angle-ply composite shafts, Machine Dynamics Problems, 6 (1993) 141-156.
• 6. A. Tylikowski, Stochastic stability of rotating composite shafts with Brazier's effect, In: Nonlinear Science, B, 7, Chaos and Nonlinear Mechanics, ( Chua L. O., ed.), World Scientific, Singapore 1994.
• 7. A. Tylikowski, Influence of torque on dynamic stability of composite thin-walled shafts with Brazier’s effect, Mechanics and Mechanical Engineering, 1 (1997) 145-155.
• 8. A. Tylikowski, Dynamic stability of weak equations of rectangular plates, J. Theor. Appl. Mech., 46 (2008) (in print).