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An active control strategy for vibration control of an axially translating beam. (English) Zbl 1349.93196
Summary: Axially translating beams are widely seen in engineering applications. An active vibration control strategy based on a modified fuzzy sliding mode control is developed for controlling and stabilizing the motion of the beam. Geometric nonlinearity of the beam is considered. In the development of the control strategy, the governing equation of the beam is transformed into a multi-dimensional dynamic system with the Galerkin method of 6th order. An active control strategy is developed corresponding to the dynamic system, such that the control strategy can be used for multi-dimensional systems. Numerical simulations are performed with application of the control strategy developed. The effectiveness of the active control strategy is demonstrated in controlling and stabilizing the chaotic motion of the translating beam.

MSC:
93C20 Control/observation systems governed by partial differential equations
74H45 Vibrations in dynamical problems in solid mechanics
93C42 Fuzzy control/observation systems
70Q05 Control of mechanical systems
93B40 Computational methods in systems theory (MSC2010)
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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