The Analysis of Stability of Weak Solutions of Circular Plate

• Autorzy: Jama D. , Czech D. , Szopa M.
• Języki publikacji: EN

Abstrakty

EN

Stability of parametric vibrations of a circular plate has been discussed for equations which describe the dynamics of a circular plate in weak formulation. A weak form of dynamic equations of mechanical structures has been derived applying the calculus of variation. Nearly definite asymptotic balance stability of a circular plate, without prior digitizing, has been analyzed in accordance with direct Lyapunov's method. The method of stability analysis has been worked out for the dynamic problems of a circular plate taking into account boundary conditions corresponding to the simple supported, the clamped and free edges. Sufficient stability conditions have been determined without involving the third and the fourth derivatives of solutions.

Słowa kluczowe

EN

weak formulation; stability conditions; Lyapunov method

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2009
• Tom: Vol. 33, No. 3
• Strony: 25--41
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr.

Twórcy

autor

Jama D.

autor

Czech D.

autor

Szopa M.

• Silesian Technical University. Institute of Mathematics,

Bibliografia

• Banks, H.T., Fang, W., Silcox, RJ., 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., 2008, Dynamic stability of weak equations of rectangular plates, Journal of Theoretical and Applied Mechanics, 46, 679-692.
• Tylikowski, A., 2008, Stability Analysis of Continous Systems with Imperfect Boundary Conditions in a Weak Formulation, Machine Dynamics Problems, 32, 3, 107-116.
• Tylikowski, A., 2008, Stability of rotating shafts in a weak formulation, J. Theor. Appl. Mech., 46, 993-1007.
• Tylikowski, A., 2008, Dynamic stability of the weak equations of continuous systems (original title in Polish: Dynamiczna stateczność słabych równań układów ciągłych), Czasopismo Techniczne Mechanika, Zeszyt 1, 241-247.
• Tylikowski, A., 2009, Dynamic stability of weak equations of continuous systems. Arch. Appl. Mech., 79, 659-665.
• Tylikowski, A., Hetnarski, R.B., 1996, Thermally induced instability of laminated beams and plates. ASME J. Appl. Mech., 63, 884-890.