Abstract
ABSTRACTThis paper studies the well-posedness and exponential stability of two-dimensional vibration model of a curved beam with tip mass under linear boundary control. The control task is to stabilise the tangential and radial vibrations, which are coupled due to the beam curvature. To reach the main results of the paper, mathematical analyses based on the semigroup theory and Lyapunov approach are conducted, and it is shown that the proposed closed-loop model holds a unique solution that converges to zero exponentially fast. These analyses are based on a hybrid dynamic model that incorporates two coupled partial differential equations and six boundary conditions, including two ordinary differential equations. Simulation results are used to illustrate the efficacy of the suggested method.
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