VIBRATION AND BUCKLING OF A STEPPED BEAM

The fundamental frequencies and the critical buckling loads of simply supported beams with stepped variation in thickness are computed using two algorithms based on the Rayleigh-Ritz method. The first algorithm, which has been used extensively in analyzing beams with non-uniform thickness, involves using a series of assumed functions that satisfy only the external boundary conditions and disregard the presence of the step. The second algorithm considers a beam with a step as two separate beams divided by the step. Two different sets of admissible functions which satisfy the respective geometric boundary conditions are assumed for these two fictitious sub-beams. Geometric continuities at the step are enforced by introducing artificial linear and torsional springs. Numerical results using these two algorithms are compared for simply supported beams with various step ratios.