ABSTRACT
Chi et al. investigated the flexural and torsional vibration of axially-loaded uniform beams for the general case of ends elastically restrained against rotation so that the usual end-conditions could be treated as particular cases. More recently, Auciello introduced two different approaches to determine the free vibration frequencies of tapered beams and beams with discontinuous cross-section, in the presence of axial loads. The first method based on the Rayleigh-Ritz approach gives the upper bound values of the frequencies. In the second method, the structure is reduced to rigid elements connected together by elastic hinges, and lower bounds to the true frequencies are obtained. The Barcilon-Gottlieb transformation was used to transform the governing differential equation of a non-uniform beam in transverse vibration. Coefficients in the transformed equation were then equated with those of the governing equation of an axially-loaded uniform beam to obtain the mass and stiffness distribution of isospectral beams.
