Abstract
The wave equation in one dimension approximately represents the longitudinal motion of a uniform bar that carries regularly spaced equal point masses. Fourier analysis is used to obtain the steady-state solution when the bar is reciprocated from one end. Distributed damping is considered.
The more general system of unequal and irregularly spaced point masses on a bar consisting of sections of different mass per unit length is analysed in terms of reflection and transmission coefficients; a wave reflection method and a transfer matrix method are given for the solution of the problem of reciprocation. The limitation of the approximate equation of motion is assessed by examining wave dispersion in the uniform system.
Application to ‘traverse bars’ on machines for winding extruded synthetic fibre was the object of the investigation.
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