Wave Propagation and Scattering in Structural Networks

Abstract

A theoretical procedure is described for the dynamic response analysis of engineering structures composed of interconnected slender members. Each structural member is treated as a multichannel waveguide, and the entire structure is treated as a network of such waveguides. Three types of analytical building blocks are then discussed: an individual waveguide, a junction where several waveguides intersect, and a boundary where either zero displacements or zero forces or their combination must be imposed. It is shown that the properties of each type of building block may be characterized by a wave‐scattering matrix that relates the incoming waves to the structural element in question and the outgoing waves from the structural element. The use of wave‐scattering matrices guarantees that numerical computation is always stable, since the computation follows the direction of wave propagation, and the wave amplitude can only decrease with the propagation distance. The proposed analytical procedure is efficient in computation and it yields very accurate results, especially if motions at specific locations on a structure are required. An example is included for illustration.