Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body

The coupled axial-bending vibration of an axially functionally graded Timoshenko cantilever beam of non-uniform cross-section is considered. The coupling phenomenon appears due to the presence of the transverse eccentricity of the mass centre of a rigid body attached to the beam free end. To study the coupled phenomenon, an approach based on the symbolic-numeric method of initial parameters is proposed. The influence of the transverse eccentricity on the cantilever beam natural frequencies and mode shapes is examined. The approach has the potential to be also applied to vibration problems of the systems composed of rigid bodies interconnected by non-uniform non-homogeneous beams.