Observation of Elastic Wave Localization
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OBSERVATION OF ELASTIC WAVE LOCALIZATION LING YE, GEORGE CODY, MINYAO ZHOU, PING SHENG AND ANDREW NORRIS. Exxon Research & Engineering Co., Annandale, NJ 08801 *Rutgers University, Department of Mechanical & Aerospace Engineering, Piscataway, NJ 08855
ABSTRACT Spatial localization of bending waves was observed on a steel plate (72"X72"X1") decorated with lucite blocks (3.5"X3.5"X3") arranged in either a periodic or a random array. The exponential decay length of the localized modes is as short as 12 cm at 2.8 kHz, and increases with frequency as (f0 - f)-1, where fo = 3.5 kHz is a quasi-mobility edge. The experimental data and finiteelement calculations suggest that the observed localization of bending waves is due to the strong resonant scattering of bending waves by the shear modes of lucite/steel system. The generic nature of this localization phenomenon suggests its potential use as a attenuation mechanism for bending waves.
The concept of wave localization was first proposed by Anderson in the context of electronic transport in disordered material.[11 Over the past three decades, the importance of the localization concept in the physics of electronic transport and the metal-insulator transition has been extensively documented.[ 2 ] However, Anderson localization has eluded direct observation in electronic systems due to inherent difficulties in mapping electronic wave functions as well as distinguishing Anderson localization from electronelectron interactions and many-body phenomena. The fact that these complexities are absent in classical wave systems is one of the reasons for the current interest in elastic wave and light localization. [3-5] The spatial dimensionality of the system is a critical parameter in the study of wave localization. In the Anderson theory, waves in one- or twodimensional systems exhibit localization for any degree of disorder.[6J In three dimensions, waves can be localized in some frequency regimes but delocalized in others. Frequencies separating the regimes in 3D are denoted as "mobility edges". The bending wave is a special type of wave which only propagates in a plate, but which includes both longitudinal and transverse displacements, and which is dispersive. The bending wave is generated by acoustic waves obeying the full compressional and shear wave equations,[ 7] but its properties can also be derived by simple mechanical models when the plate thickness is considerably smaller than the bending wavelength. The propagation of bending waves in smooth plates has been extensively studied.1 8] The subject of this paper is the first examination of 2D propagation of bending waves in randomly or Mat. Res. Soc. Symp. Proc. Vol. 253. 01992 Materials Research Society
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periodically rough composite plates. We have discovered a strong resonant scattering of the bending waves which leads to spatial localization of the bending wave over a broad frequency range and where the localization phenomenon exhibits a "quasi-mobility edge" in frequency characteristic of 3Dlocalization. The experi
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