Optimal damping of the infinite-dimensional vibrational systems: commutative case
作者： Ivica Nakić
DOI: 10.3336/GM.48.2.10
关键词:
摘要: In this paper we treat the case of abstract vibrational system form $M\ddot{; ; x}; +C\dot{; +x=0$, where positive semi- definite selfadjoint operators $M$ and $C$ commute. We explicitly calculate solution corresponding Lyapunov equation which enables us to obtain set optimal damping operators, thus extending already known results in matrix case.
core.ac.uk
sci-hub.st 参考文章(11)
Krešimir Veselić, Katrin Brabender, Krešimir Delinić, Passive Control of Linear Systems ,(2011)
P. Benner, Z. Tomljanović, N. Truhar, Dimension Reduction for Damping Optimization in Linear Vibrating Systems Journal of Applied Mathematics and Mechanics. ,vol. 91, pp. 179- 191 ,(2011) , 10.1002/ZAMM.201000077
Richard Datko, Extending a theorem of A. M. Liapunov to Hilbert space Journal of Mathematical Analysis and Applications. ,vol. 32, pp. 610- 616 ,(1970) , 10.1016/0022-247X(70)90283-0
Timo Veijola, Analytic damping model for an MEM perforation cell Microfluidics and Nanofluidics. ,vol. 2, pp. 249- 260 ,(2006) , 10.1007/S10404-005-0072-5
Steven J. Cox, Ivica Nakić, Annette Rittmann, Krešimir Veselić, Lyapunov optimization of a damped system Systems & Control Letters. ,vol. 53, pp. 187- 194 ,(2004) , 10.1016/J.SYSCONLE.2004.04.004
Ninoslav Truhar, Krešimir Veselić, An Efficient Method for Estimating the Optimal Dampers' Viscosity for Linear Vibrating Systems Using Lyapunov Equation SIAM Journal on Matrix Analysis and Applications. ,vol. 31, pp. 18- 39 ,(2009) , 10.1137/070683052
Falun Huang, On the Mathematical Model for Linear Elastic Systems with Analytic Damping SIAM Journal on Control and Optimization. ,vol. 26, pp. 714- 724 ,(1988) , 10.1137/0326041
Ninoslav Truhar, An efficient algorithm for damper optimization for linear vibrating systems using Lyapunov equation Journal of Computational and Applied Mathematics. ,vol. 172, pp. 169- 182 ,(2004) , 10.1016/J.CAM.2004.02.005
S. J. Cox, Designing for Optimal Energy Absorption, 1: Lumped Parameter Systems Journal of Vibration and Acoustics. ,vol. 120, pp. 339- 345 ,(1998) , 10.1115/1.2893836
Shu Ping Chen, Roberto Triggiani, PROOF OF EXTENSIONS OF TWO CONJECTURES ON STRUCTURAL DAMPING FOR ELASTIC SYSTEMS Pacific Journal of Mathematics. ,vol. 136, pp. 15- 55 ,(1989) , 10.2140/PJM.1989.136.15