ABSTRACT
Consider now a typical eigensolution pair ,, A where ' is a set of field quantities (displacements and forces). If this set of field quantities were prescribed as acting on the left face of segment i the response on the left face of the following segment (i + l) would be the identical set of field quantities multiplied by the complex scalar A.. The field quantities are all scaled in magnitude and shifted in phase uniformly. Thus,, A describe in general a propagating wave where ' describes the relative solid and fluid displacements at a cross section and A is the associated propagation constant. The propagation constant (plus frequency and segment length) then yields the associated phase speed and attenuation constant. The dynamic matrix D may be of arbitrarily large order and hence the number of possible eigensolution pairs may be similarly arbitrarily large. However, at a given frequency, the structure possesses only a finite set of valid propagating wave forms. These are detected simply by examination as the valid propagating wave forms have the following propenies:
l . occur as a complex conjugate pair describing both forward and backward propagating waves.
