Free vibrations of continuous beams with singularities in inertia and stiffness distribution

The free vibrations of continuous beams with singularities in inertia and stiffness distribution are presented in this paper. Simple closed-form mathematical expressions for the mode shapes of vibrations are obtained using Galerkin's approach. Several numerical examples of structures with known exact solutions are presented to show the accuracy of the method. Also, examples of a simple beam with intermediate elastic translational and rotational supports carrying point and rotational mass, a two-span continuous beam with variable moment of inertia and mass distribution and a single-span beam with fixed end and overhanging cantilever are presented to show the applicability of the method