Vibration Analysis of Curved Beam Using Higher Order Shear Deformation Theory with Different Boundary Conditions

The vibration analysis of isotropic curved beam having different end conditions (i.e., c-c and s-s) with different L/R ratios using higher order shear deformation theory is the main focus of this paper. The dependence of boundary conditions and radius of curvature on the frequency response are highlighted. It was found that the convergence result of the beam that for L/R = 0.0625 the convergence is more rapid for clamped-clamped condition of the beam than that of simply supported beam. The value of frequency of vibration for clamped-clamped beam is higher compared to simply supported beam having L/R = 0.0625. Similarly, the value of frequency of vibration for clamped-clamped beam is higher compared to simply supported beam having L/R = 0.125. If we observe the values of frequency of vibration for beam having L/R = 0.25, the convergence is more rapid for clamped-clamped beam compared to simply supported beam. It goes from 2300 to 773 rad/s when the number of element changes from 50 to 800 for C-C condition and 1500 to 494 rad/s for the same value of number of elements. Thus, we observe that as R is decreased keeping L constant the value of frequency of vibration increases. It was also observed that as the boundary conditions are changed from clamped-clamped to simply support the frequency also decreases for same L/R ratio.