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Section B

Two-sided bounds for the asymptotic behaviour of free nonlinear vibration systems with application of the differential calculus of norms

Pages 653-667 | Received 16 May 2007, Accepted 26 Mar 2008, Published online: 07 Oct 2008
 

Abstract

This paper deals with the free nonlinear dynamical system [xdot](t)=A x(t)+h(t, x(t)), tt 0x(t 0)=x 0, where A is an n×n-matrix and h a nonlinear vector function with h(t, u)=o(∥u∥). As the first novel point, a lower bound for the asymptotic behaviour on the solution x(t) is derived. Two methods are applied to determine the optimal two-sided bounds, where one of the methods is the differential calculus of norms. In this context, the second novel point enters; it consists of a new strategy to significantly reduce the computation time for the determination of the optimal constants in the two-sided bounds. The obtained results are especially of interest in engineering and cannot be obtained by the methods used so far.

2000 AMS Subject Classification :

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