As a baseline for treating flexible beam attached to central-body space structure, the generic problem of a cantilevered Euler-Bernoulli beam with piezoelectric actuator attached as appropriate along the beam and its control is solved in great detail. The baseline approach can be utilized to solve more complex problems in engineering and in the selection and utilization of commercial software. For comparative study, three generic configurations of the combined beam and piezoelectric elements are solved, which could be used in further works for feasible applications. For simplicity, Euler-Bernoulli theory is utilized to solve the free vibration of the beam by both analytical and numerical methods. The equation of motion of the beam is obtained by using Hamilton's principle, and the baseline problem is solved using finite element method. An in-house computational routine is developed for various applications. Euler-Bernoulli theory;Finite Element Method;Hamiltonian Mechanics;Piezoelectric Material;Active Vibration Control;Structural Dynamics.
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