Stability Analysis of Continuous Systems with Imperfect Boundary Conditions in a Weak Formulation

• Autorzy: Tylikowski A.
• Konferencja: International Conference on Modelling and Simulation of the Friction Phenomena in the Physical and Technical Systems "FRICTION 2008" (5 ; 31.05-1.06.2008 ; Warsaw, Poland) ; French-Polish Seminar of Mechanics (16 ; 31.05-1.06.2008 ; Warsaw, Poland)
• Języki publikacji: PL

Abstrakty

EN

Dynamics of continuous systems have been considered in a weak (variational) form. Dynamics equation of beam subjected to the axial stochastic force in the weak formulation has been derived. The weak form of dynamics equations of linear mechanical structures is obtained using variational calculus. The almost sure stochastic stability of beam equilibrium, without the previous discretization, has been analysed by means of direct Lyapunov method. The stability analysis method is developed for distributed dynamic problems with relaxed assumptions imposed on solutions. Sufficient stability conditions have been established for the imperfect boundary conditions and two limit cases: the simply supported beam and the clamped beam are obtained.

Słowa kluczowe

PL

drgania parametryczne; metoda Lapunowa; warunki brzegowe

EN

weak formulation; parametric vibration; stability conditions; Lyapunov method; imperfect boundary conditions

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2008
• Tom: Vol. 32, No. 3
• Strony: 107--116
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Tylikowski A.

• Warsaw University of Technology. Institute of Machine Design Fundamentals,

Bibliografia

• Banks, H. T., Fang, W., Silcox, R. J., Smith, R. C., 1993, Approximation methods for control of structural acoustics models with piezoelectric actuators, Journal of Intelligent Material Systems and Structures, 4, 98-116.
• Kozin, F., 1972, Stability of the linear stochastic system, Lecture Notes in Mathematics, 294, 186-229.
• Tylikowski, A., 2005, Stabilization of plate parametric vibrations via distributed control, J. Theor. Appl. Mech., 43, 695-706.
• Tylikowski, A., 2008a, Dynamic stability of weak equations of continuous systems, Archive of Applied Mechanics, 78, 49-60.
• Tylikowski, A., 2008b, Dynamic stability of weak equations of rectangular plates, J. Theor. Appl. Mech., 46, 679-692.
• Tylikowski, A., 2008c, Dynamic stability of weak continuous systems (original title in Polish: Dynamiczna stateczność słabych równań układów ciąłych), Czasopismo Techniczne, Mechanika, Zeszyt 1, 241-247.
• Tylikowski, A., 2008d, Stability of rotating shafts in a weak formulation, J. Theor. Appl. Mech., 46, 993-1007.
• Tylikowski, A., Hetnarski, R. B., 1996, Thermally induced instability of laminated beams and plates, ASME J. Appl. Mech., 63, 884-890.