Free Vibrations of Horizontally Curved Beams

수평 곡선보의 자유진동 해석

The differential equations governing free, out of plane vibrations of horizontally curved beams are derived and solved numerically to obtain the natural frequencies and the mode shapes. The Runge-Kutta method and Regula-Falsi method are used to integrate the differential equations and to determine the natural frequencies, respectively. In nu- merical examples, the hinged-clamped end constraint is considered and four lowest frequency parameters are reported as functions of four non-dimensional system parameters: (1) opening angle, (2) slenderness ratio, (3) shear parameter and (4) stiffness parameter. Also, typical mode shapes of displacements and stress resultants are shown.