Free vibration analysis using the transfer-matrix method on a tapered beam

A transfer-matrix method is developed to determine more accurate solutions to the free vibration characteristics of a tapered Bernoulli-Euler beam. The roots of the differential equation are determined by using the Frobenius method to obtain the power series solution for bending vibrations. This study examines the effect of various taper ratios on the eigenpairs of these beams, in which the height of the cross-section along the length is linearly reduced. In addition, the number of terms in the power series is investigated in detail for each taper ratio because the required number of terms depends upon the taper ratio.