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