Wave scattering phenomena around intermediate constraints of one-dimensional structures.

A recent paper by Yong and Lin [Y. Yong and Y. K. Lin, J. Sound Vib. 129, 99–118 (1989)] has shown that the wave propagation approach is the most suitable technique to study the vibration of one-dimensional structures. In this method, a structure is treated as a waveguide and vibration motion is modeled as wave transmissions in uniform media and reflections at boundaries and interfaces between distinct materials. However, many structures in reality contain different intermediate constraints, such as static supports, rollers, internal hinges, and elastic supports. These constraints do cause significant difficulties in the analysis. In this paper, attention is focused on the wave scattering phenomena around intermediate constraints and their effects to the free and forced vibrations. The study concludes, for the first time, that any intermediate constraint can serve as a waveguide capable of transmitting and reflecting waves in either direction. This new finding enables us to treat the original structure as an equivalent one-dimensional structure without constraints, which can be handled easily by using the wave propagation approach. The new technique proposed in this paper is superior over other existing methods, such as transfer matrix and finite-element methods, in terms of accuracy, efficiency, simplicity, and generality. [Work supported by NSF.]