EFFECTS OF ROTARY INERTIA AND SHEAR DEFORMATION ON EXTENSIONAL VIBRATIONS OF CONTINUOUS CIRCULAR CURVED BEAMS
This dissertation is devoted to the dynamic analysis of continuous circular curved beams. The dynamic stiffness matrix is derived for the determination of natural frequencies of continuous curved beams undergoing in-plane vibrations. The formulation of stiffness matrix may be widely applied to problems with various consideration of Bernoulli-Euler Theory, Rayleigh Theory and Timoshenko Theory. Using this formulation for dynamic loading, the fixed-end moment, shear and thrusts for concentrated and distributed loads have been derived. Two continuous circular curved beams subjected to free and forced vibrations are given to illustrate the application of the proposed method and to show the effects of rotary inertia, shear deformation, axial deformation, frequency of the applied load and the central angle of the arc on the beams.
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