Abstract
This paper describes the free and forced motion of two, thin, concentric, circular cylindrical shells joined at their ends by rigid diaphragms with inertial properties. Mathematically the problem is described by two special Sturm-Liouville systems with common eigenvalues coupled only through the boundary conditions. The systems possess a modified orthogonality principle and give rise to a modified expansion principle for the associated non-homogeneous systems. These principles are derived in detail and several free motion problems are presented to illustrate the theory.
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