An ideal periodic structure is one which is constructed by connecting together identical units. Since manufacturing inaccuracy and material inhomogeneity are always present in practice, ideal periodic structures never actually exist. The term "disorder" is used here to indicate the departure from a perfect periodicity. The present paper explores the effect of random span-length deviations of an otherwise perfect periodic beam on many hinge supports as manifested by the random values of frequency response functions. Two types of excitation are considered. The first is either a concentrated force or a concentrated moment. The second is a frozen force distribution convected at a constant velocity. Four types of response are treated simultaneously, including deflection, slope, moment and shear at any location on the beam. It is shown that the magnitude of the statistical average of a frequency response function can be considerably greater than the value computed without taking into account the disorder in span lengths, especially near the frequencies of resonance. Also, near these frequencies the standard deviation of a frequency response function becomes quite large, indicating greater uncertainty in such regions. Furthermore, in the case of convected loading the use of a perfect periodic model cannot account for the response in certain vibration modes while these modes can be actuated in a disordered system.