Resonance blocking and passing effects in two-dimensional elastic waveguides with obstacles

Resonance localization of wave energy in two-dimensional (2D) waveguides with obstacles, known as a trapped mode effect, results in blocking of wave propagation. This effect is closely connected with the allocation of natural resonance poles in the complex frequency plane, which are in fact the spectral points of the related boundary value problem. With several obstacles the number of poles increases in parallel with the number of defects. The location of the poles in the complex frequency plane depends on the defect's relative position, but the gaps of transmission coefficient plots generally remain in the same frequency ranges as for every single obstacle separately. This property gives a possibility to extend gap bands by a properly selected combination of various scatterers. On the other hand, a resonance wave passing in narrow bands associated with the poles is also observed. Thus, while a resonance response of a single obstacle works as a blocker, the waveguide with several obstacles becomes opened in narrow vicinities of nearly real spectral poles, just as it is known for one-dimensional (1D) waveguides with a finite number of periodic scatterers. In the present paper the blocking and passing effects are analyzed based on a semi-analytical model for wave propagation in a 2D elastic layer with cracks or rigid inclusions. (C) 2011 Acoustical Society of America. [DOI: 10.1121/1.3592225]