Integral transforms

The effect of traveling wave blocking by a system of obstacles is widely used in various areas, such as vibrodamping, anti-seismic protection, opto- and microelectronics, etc. The effect manifests itself as deep gaps in the frequency spectra of transmitted signals. The gap band appearance is especially sound in periodic structures, e.g., with systems of interdigital contacts or grooves used in acoustoelectronic technology, in periodic composites, phononic lattices, and photonic crystals. On the other hand, a resonant shielding of traveling waves by one or more obstacles is known as a trapped mode effect. This effect features the capture and localization of time-averaged wave energy of a time-harmonic wave field in the form of energy vortices. The trapped mode effect is closely connected with the allocation of spectral points (poles) of the corresponding boundary value problem, which are natural frequencies of the waveguide with obstacles. The closer a pole is located to the real axis, the more the trapped mode effect becomes apparent. Besides the blocking ability, the resonance response of hidden defects can be used for nondestructive testing purposes, e.g., for guided wave crack and delamination detection in metallic and composite laminate plates.