전단변형(剪斷變形)을 고려한 수평(水平) 곡선(曲線)보의 자유진동(自由振動)

Free Vibrations of Horizontally Curved Beams with Shear Deformation

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effect of shear deformation as well as the effects of vertical, rotatory and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported, with and without the effect of shear deformation, as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio and the stiffness parameter.