In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the Ritz-Kantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two 'extreme' cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.
Indri, M., Tornambè, A. (1996). Lyapunov analysis of the approximate motion equations of flexible structures. SYSTEMS & CONTROL LETTERS, 28(1), 31-41 [10.1016/0167-6911(96)00007-2].
Lyapunov analysis of the approximate motion equations of flexible structures
Tornambè, Antonio
1996-01-01
Abstract
In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the Ritz-Kantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two 'extreme' cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
