Natural Vibrations of a Tapered Beam

Abstract

This is a theoretical and experimental study of natural frequencies of bending vibrations of a beam with non-uniform cross section. General solution of the differential equation of the eigenvalue problem has been obtained by making use of power series solutions. This solution is applied to a uni-tapered cantilever with I-type cross section, and the nondimensional frequency equation is introduced, yielding a good coincidence of the numerical computations with experimental values concerning the natural frequencies. Secondly, a uni-tapered beam with rectangular cross section supported at two intermediate points is taken up, giving a nondimensional frequency equation. Numerical results are compared with those obtained by the Frobenius method, demonstrating the superiority of the series solution to the Frobenius method.