Class of analytical closed-form polynomial solutions for clamped–guided inhomogeneous beams

New closed-form solutions for the natural frequency of a clamped–guided beam are derived in this investigation. By postulating the mode shape of the clamped–guided beam, whose material density and stiffness are taken as polynomial functions, one is able to calculate the closed-form solution for its natural frequency. A remarkable property of the suggested method is its extreme simplicity.