Abstract
Consideration is given to determining the exact natural frequencies and modes of vibration of a class of structures comprising two parallel members with uniform distribution of mass and stiffness, which have independent properties and which are linked to each other, and possibly also to foundations, by uniformly distributed elastic interfaces of unequal stiffness. The formulation is general and applies to any structure in which the motion of the component members is governed by a second order linear differential equation. Closed form solution of the governing differential equations leads either to an exact dynamic stiffness matrix or to a number of exact relationships between the natural frequencies corresponding to coupled and uncoupled motion. An appropriate form of the Wittrick-Williams algorithm is presented for converging on the required natural frequencies to any desired accuracy. Examples are given to confirm the accuracy of the approach and to indicate its range of application.
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