Dr. Oleg N. Kirillov
Institute of Mechanics
Moscow State Lomonosov University
Moscow, Russia
E-mail: kirillov@imec.msu.ru
We consider a non-conservative system governed by the equation y''+Ay=0, where A is a real non-symmetric m-by-m matrix smoothly dependent on a vector of n real parameters p=(p1,...,pn). At the fixed p this system is stable if and only if all the eigenvalues of the matrix A are positive and semi-simple. If the spectrum of A contains a complex conjugate pair then the system loses stability dynamically (flutter). Characteristic curve is a dependence of an eigenvalue of the matrix A on a chosen parameter, say on p1, while other n-1 parameters remain fixed. Characteristic curves of the stable system lie on the real plane. We define a functional of the critical load F as a minimal value of the parameter p1>=0 at which the flutter instability occurs. The optimization problem is to maximize F due to change of parameters p2,...,pn.
It turns out that due to change of parameters p2,...,pn any two
characteristic curves of the stable system corresponding to positive
simple eigenvalues may come together, merge at some point, and then
overlap forming a closed curve of the complex eigenvalues (flutter
instability) on some range of the parameter p1
This work was done jointly with Alexander P. Seyranian.
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Last update: November 14, 2002 by
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