Vibration analysis of horizontally curved beams with warping using DQM

The differential quadrature method (DQM) is applied to computation of the eigenvalues of small-amplitude free vibration for horizontally curved beams including a warping contribution. Natural frequencies are calculated for single-span, curved, wide-flange uniform beams having a range of nondimensional parameters representing variations in warping stiffness, torsional stiffness, radius of curvature, included angle of the curve, polar mass moment of inertia, and various end conditions. Results are compared with existing exact and numerical solutions by other methods for cases in which they are available. The DQM provides accuracy even when only a limited number of grid points is used. In addition, results are given for a cantilever that has one clamped end and one free end; no previous results are known for this case. Finally, parametric results are presented in dimensionless form.