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A Numerical Study for a Flexible Euler-Bernoulli Beam with a Force Control in Velocity and a Moment Control in Rotating Velocity
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In this paper, we numerically study a flexible Euler-Bernoulli beam with a force control in velocity and a moment control in rotating velocity. First, we show the existence and uniqueness of the weak solution using Faedo-Galerkin’s method with the intermediate spaces. Then, we use the finite elements method with the cubic Hermite polynomials for the approximation of (1.1)–(1.5) in space such that the semi-discrete scheme obtained is stable and convergent. In addition, an a-priori error estimate is obtained. Finally, we perform numerical simulations in order to validate this method.
Keywords
Beam Equation, Existence and Uniqueness, Higher Regularity, Finite Element Method, Galerkin Method, Priori Estimates.
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