A power series solution for rotating nonuniform Euler-Bernoulli cantilever beams

A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beamwith an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differentialequation describing the vibration problem is first written as a first-order matrix differential equation, which is then solvedusing the power series method. The method can be used to obtain an approximate solution of vibration problems fornonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness ofthe method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapesand frequency parameters were found to be in satisfactory agreement with previously published results. The effects oftapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone