Normal vibration frequencies of two- and three-dimensional arrays of alternating point masses

Document Type

Article

Publication Date

4-22-1976

Department

Department of Physics

Abstract

Normal vibration frequencies are calculated for alternating point-masses of mass M and m in two-dimensional rectangular and a three-dimensional parallelepiped arrays. The method of intermediate co-ordinate transformation is used in the analysis. In applying this method, the vibrating systems consisting of alternating masses are treated as the basic systems of linear chains of identical point-masses of mass m (the zero-order system) that are coupled together to form the two- and three-dimensional systems and then further modified by inclusion of an additional mass εm at alternating sites, where M = (1 + ε)m. The zero-order solution for the linear array of identical particles of mass m is well known. The present calculation shows the advantage of the process of intermediate co-ordinate transformation in simplifying problems which are otherwise complicated and also illustrates how such a process can be applied in more than one successive step.

Publisher's Statement

© 1976

Publication Title

Journal of Sound and Vibration

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