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Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.

This paper uses the singular value decomposition approach to find the optimal distribution of a set of piezoelectric actuators and sensors in order to suppress the vibrations of a thick plate. The dynamic model of the system is derived using Mindlin plate theory and consequently, the finite difference method is employed to divide the thick plate to a finite number of nodes with appropriate horizontal and vertical distances. To compute the control force of piezoelectric actuators, the singular value decomposition approach for the column control matrix is supposed as the fitness function of an optimization problem. Through a genetic algorithm, the optimized solution is obtained. The results of numerical simulations indicate the optimal location achieved by the proposed method outperforms the previous results in suppressing the vibrations of a thick plate.