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

In this study, new closed-form solutions for the natural frequency are deri ved for a beam guided at one end and pinned at the other end. As in Elishak off and Guede (cf. Elishakoff I, Guede Z. Family of analytical polynomial s olutions for simply supported inhomogeneous beams, part 1: vibration. Journ al of Sound and Vibration 2000, to appear.), we preselected a function that is postulated to be the mode shape of the beam. Then, the stiffness and th e material density are taken as a polynomial function of specific order. Fi nally, from the governing equation of a vibrating beam, we express new clos ed-form solutions for the natural frequency. (C) 2001 Elsevier Science Ltd. All rights reserved.