Wave propagation in multiply connected deep waveguides

Abstract

The longitudinal dynamics of a deep waveguide segment is recast such that the description requires information only at its end points. This is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements. The analysis gives the exact frequency dependent response for the waveguide segment irrespective of its length. By combining these results with a previously presented spectral formulation for the flexural dynamics of a deep (Timoshenko) beam, a spectral formulation for the dynamics of multiply connected waveguides forming frames is obtained. Examples of its use in analyzing wave propagation in connected structures are given and compared with results from a two-dimensional finite element analysis.