Objective functions in monocriterial and multicriterial optimizations problems against a loss of dynamic stability

• Autorzy: Foryś A. , Snamina J.
• Języki publikacji: EN

Abstrakty

EN

The paper concerns the specification and comparison of numerical examples of optimization of beams in the state periodic parametric resonance with respect to different measures of the phenomena considered, i.e., with respects to different optimization criteria - some objective functions in monocriterion and multicriterial optimization. A formulation of monocriterion and multicriterial optimization problems. for mechanical elements, subjected to paramatricallyexciting force periodic in time, is given. In multicriterial optimization the scalar objective functions characterizing the parametric resonance are introduced. The paper deals with the problems of finding the control function - function of the shape (the area of cross-section of the beam) which maximizes or minimizes the objective functions under the constraint of constant volume. In some cases the optimization problems under conditions of parametric resonance reduce to the optimization problems with respect to natural frequency. The examples of parametric optimization against loss of stability are solved and analysed.

Słowa kluczowe

EN

optimization; dynamic stability

PL

optymalizacja; stateczność dynamiczna

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2000
• Tom: Vol. 48, iss. 1
• Strony: 73--94
• Opis fizyczny: Bibliogr. 19 poz., rys., tab., wykr.

Twórcy

autor

Foryś A.

• Cracow University of Technology Poland

autor

Snamina J.

• Cracow University of Technology Poland

Bibliografia

• 1. W.W. BOLOTIN, Dynamic stability of elastic systems, (translation from the Russian), San Francisco: Holden-Day 1964.
• 2. M.P. CARTMELL, Introduction to linear, parametric and nonlinear vibrations, London, Chapman and Hall 1990.
• 3. R.A. IBRAHIM et al., Parametric vibrations, The Shock of Vibration Digest, 10, 1, 1978: Part I: Mechanics of linear problems, 10, 2, 15–29; Part II: Mechanics of nonlinear problems, 10, 3, 9–14; Part III: Current problems (1), 10, 4, 41–57; Part IV: Current problems (2), 10, 4, 19–47, 1978.
• 4. L. ADLER, Parametric phenomena in physics, Am. J. Phys., 39, 1522–1527, 1971.
• 5. W. SZEMPLINSKA-STUPNICKA, Problems of parametrical vibrations in dynamics of machines, [in:] Contemporary problems of machine dynamics, PAN 1976.
• 6. L. RUBY, Applications of Mathieu equation, Am. J. Phys., 64, 1, 1996.
• 7. H. WINTER and H. W. ORTJOHANN, Simple demonstration of storing macroscopic particles in a "Paul trap", Am. J. Phys., 59, 9, 1991.
• 8. C. SACKETT, E. CORNELL et. al., A magnet suspension system for atoms and bar magnets, Am. J. Phys., 61, 4, 1993.
• 9. A. FORYŚ, On an objective function in optimization problems with a loss of dynamic stability, J. Theor. Appl. Mech., 30, 1, 1992.
• 10. FORYŚ, Variational optimization problems against a loss of dynamic stability, Structural Optimization, 8, 1994.
• 11. FORYŚ, Optimization of mechanical systems in conditions of parametric resonance and in autoparametric resonances, Cracow University of Technology, 1996.
• 12. FORYŚ, Optimization of parametrically excited mechanical systems against loss of dynamic stability, J. Sound Vibr. (in print), 1998.
• 13. FORYŚ and J. SNAMINA, Multicriterial optimization of parametrically excited systems against loss of dynamic stability, Structural Optimization, 16, 4, 1998.
• 14. N.W. BANICHUK, S. IVANOVA and A.W. SHARANYUK, Dynamics of structures. Analysis and optimization [in Russian], Nauka, Moskva 1989.
• 15. N. OLHOFF, Optimal design against structural vibration and instability, Technical University of Denmark, Lyngby 1978.
• 16. W.B. GRINIEV and A.P. FILIPPOV, Optimization of bars with respect of angenvalues [in Russian], 1979.
• 17. W. SZEMPLINSKA-STUPNICKA, The behaviour of non-linear vibrating systems, Dordrecht 1990.
• 18. A.S. FORYŚ and A. GAJEWSKI, Parametric optimization of a visco-elastic rod in view of its dynamic stability [in Polish], Engng. Trans., 35, 1987.
• 19. A.S. FORYŚ, Parametric optimization of a rod at different support conditions [in Polish], Engng. Trans., 38, 1990.