Normal vibrations of two parallel-coupled diatomic linear lattices: Method of intermediate coordinate transformation

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A new method of vibrational analysis (intermediate coordinate transformation) is described from a purely mechanical point of view by applying it to a system of two parallel-coupled diatomic linear lattices. The method is a modification of the method of extra forces that was presented earlier in this journal [1]. In this method, the system is regarded as a superposition of four monatomic linear chains, M-particle and m-particle chains for each lattice, coupled together to form a planar lattice model. The complete energy expressions for the system are first transformed into those in terms of the normal coordinates of the separate monatomic chains. The normal-mode solution for the system obtained from such energy expressions is the result of coupling various modes of the separate chains. Because the coupling of the modes is restricted by the symmetry properties of the normal modes, the intermediate coordinate transformation simplifies the problem. The method described here can be applied to more complicated lattice models to facilitate the analysis. © 1971.

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Journal of Sound and Vibration