Free vibrations of tapered beams with general boundary condition

Abstract

This paper deals with the free vibrations of tapered beams with the general boundary condition. The ordinary differential equation governing the free vibrations of such beams is derived, in which three kinds of taper type with the rectangular cross section are considered. For calculating both the natural frequencies and mode shapes of such beams, the governing equation is solved by numerical methods. The Runge-Kutta method is used for integrating the differential equation and the Determinant Search method combined with the Regula-Falsi method is used for calculating the natural frequencies For validation purpose, the numerical results obtained hereinare compared to those in the open literature. As the numerical results, the relationships between the frequency parameters and various beam parameters are reported in tables and figures and some typical mode shapes are presented in figures.