This paper presents a method to predict the dynamic response of a fluid conveying pipe carrying a discrete mass when the flow velocity is less than its critical value. A general expression for the normal modes of a vibrating pipe with various boundary conditions is newly derived herein. Also presented for a particular case are the numerical results of eigenfunctions and eigenvalues which can be used to calculate the dynamic response of a simply-supported pipe with an attached discrete mass at its mid-span.

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