VIBRATIONS OF A CANTILEVER TAPERED BEAM WITH VARYING SECTION PROPERTIES AND CARRYING A MASS AT THE FREE END

The free vibration frequencies of a beam composed of two tapered beam sections with different physical characteristics with a mass at its end can be determined by using either the exact procedure, for which purpose the solution to the problem can be expressed using Bessel functions, or the approximate Rayleigh–Ritz treatment, with the assumption of orthogonal polynomials as test functions. The results and the numerical comparison between the two methods are provided in diagrams and tables. The effect of different materials on vibrations modes is also provided.