Free Vibration of a Disordered Periodic Beam

Abstract

Using a first-order perturbation procedure the statistical properties of the natural frequencies and their associated normal modes of a disordered N-span beam are investigated. Two types of disorder are considered: the random deviation of span length from an ideal design value and the random fluctuation of the bending stiffness along the beam. The grouping pattern of the natural frequencies is used to establish a perfect correlation among certain random natural frequencies; therefore, their relative position can never be reversed. For other natural frequencies a sufficiency condition for nonreversal of position order is given.