ABSTRACT
This chapter deals with the vibrations of a beam that has a guided support on the left end and a pinned support on the right end. It presents a function that satisfies all boundary conditions, to serve as a mode shape of the vibrating beam and provides an inhomogeneous beam that has the postulated function as the mode shape. Research by Isaac Elishakoff and Candan deals with three other boundary conditions: pinned–clamped, clamped–free and clamped–clamped beams. The present formulation screens, as it were, the beams that have the same frequencies under differing boundary conditions. After representing the material density and the flexural rigidity too as polynomial functions, for different boundary conditions, the natural frequency of the beam was determined in a closed-form fashion. The chapter explores the degree of the polynomial function that represents the mode shape, and examines the inhomogeneous beams that have this specified function as their fundamental mode shape.
