ABSTRACT
The free, out-of-plane vibration of a rotating nonhomogeneous beam with a nonlinear spring and mass system has been analysed. The effect of nonhomogeneity of the beam appears both in the governing equations and boundary conditions, but a nonlinear spring-mass effect appears in the boundary conditions only. The solution is obtained by applying methods of multiple time scales directly to the nonlinear partial differential equations. The results of the linear frequencies match well with those available in open literature. The effect of the nonhomogeneity of the stiffer beam reduces the frequencies of the beam less than the stiff beam . This contradicts the conventional idea that a stiffer beam vibrates with higher frequencies. For this a possible explanation is provided. A subsequent nonlinear study of the nonhomogeneous beam indicates that the mass of the spring and its location have also a pronounced effect on the vibration of the beam. The effect of nonhomogeneity of the beam on the relative stability of the nonlinear vibration of the beam with spring-mass system is also studied.
