Modal-sum and image-sum procedures for estimating wide-band random response of structures

Abstract The nature of the mean-square velocity response field in one- and two-dimensional structures subjected to point excitation by wide-band random forces is described, with emphasis on the effects of damping and of excitation bandwidth. Two procedures for predicting the response are studied. Both procedures require evaluating an array of integrals. The sizes of the arrays and the relative dominance of the main-diagonal terms in the arrays are shown to depend differently on the damping, excitation and dimensionality of the structure. The modal-sum procedure is advantageous for lightly damped, two-dimensional structures excited by relatively narrow-band processes. The image-sum procedure is advantageous for heavily damped, one-dimensional structures excited by very wide-band processes. The image-sum procedure has the additional feature that it provides a simple means of locating local zones of intensification and reduction of response and estimating the magnitude of the relative intensification or reduction in such zones.