Response of a System Consisting of N Coupled Elements

Abstract

The impulse response function method, which was developed previously by Tucker and Maidanik [J. Acoust. Soc. Amer. 51, 87(A) (1972)] is extended to a system containing N-coupled elements where the coupling acts only at a point of each element. The essence of the method is that it considers the coupling to be a force field acting on an uncoupled element of the system. Then this coupling force field together with the external driving field and the impulse response functions of the uncoupled elements determines the response of the coupled system to an arbitrary external driving field. This method does not require a priori definition of the exact nature of the individual elements; it requires only the existence of the elemental impulse response function and knowledge of the type of coupling. As a specific example, the general result is utilized to investigate a system where the elements are identical, the coupling impedances are identical, the points of attachment on each element are similar, and a point driving force is applied to only one element. Then the effect on the response of the system of various degrees of coupling and the number of elements in the system is examined.