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A new method of analyzing wave propagation in periodic structures; Applications to periodic timoshenko beams and stiffened plates

Journal of Sound and Vibration
Publication Date
DOI: 10.1016/s0022-460x(86)80128-6


A response function is found for an infinite, uniform, one-dimensional structure which is subjected to an array of harmonic forces or moments, spaced equidistantly, and which have a constant phase or ratio between any adjacent pair. Receptance functions are derived for these “phased arrays”. They are used to set up a general determinantal equation for the propagation constants of the infinite structure when it is made periodic by the addition of an infinite set of regular constraints. They are also used to set up equations for the response of the structure to a convected harmonic pressure field. The method enables the equations for the propagation constants and for the response to convected loading to be set up with much greater facility than by earlier methods. It only requires a knowledge of the response function of the infinite uninterrupted structure under a single-point harmonic force or moment. The general equation for the propagation constants is used to study (a) a simply supported periodic Timoshenko beam, and (b) a parallel plate with periodic beam-type stiffeners. Some calculated propagation constants are presented and discussed. The periodic plate results are relevant to integrally stiffened skins of the type used in aeroplanes.

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