Normal Vibration Frequencies of a Rectangular Two-Dimensional Array of Identical Point-Masses

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Department of Physics


An exact solution is obtained for the normal vibration frequencies of a rectangular array of identical point-masses. The method of intermediate co-ordinate transformation, which was introduced in a previous article in this journal, makes it possible to treat the system as a coupled set of linear chains. By this means, the analysis can be made considerably simpler than the usual treatment. The result shows that the coupling of the normal modes of the separate chains is restricted to those modes having the same index numbers. Thus, the usual problem involving N1×N1 secular determinant, where N1 is the number of particles contained in each separate chain, is reduced to that involving only a 2×2 determinant. The calculation in the present article will serve as a basis for the vibrational analyses of more complicated problems involving two- and three-dimensional arrays of masses that are perturbed by "disorder".

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© 1976

Publication Title

Journal of Sound and Vibration