Two-dimensional scattering of elastic waves by periodic distribution irregularities in an elastic full space

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (14) : 201-213.

BA Zhenning1,2,GAO Xu1,LIANG Jianwen1,2

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Abstract

A periodic indirect boundary element method (PIBEM) based on the dynamic Green’s functions of uniformly distributed loads was used to study the scattering and diffraction of plane P- waves and SV-waves by periodically distributed irregular bodies in a full-space.By virtue of the fact that the dynamic responses around each of the canyons along the x-axis has the particular feature of repeating themselves with a certain delay of phase in frequency domain, the effort can be reduced to discretize and solve only a single irregular body.Compared with the method of truncating a finite number of irregular bodies for approximate solution, the method proposed in this paper has the advantages of higher precision and greater memory reduction.The accuracy of the method was verified by comparing its degenerated results with published results.Numerical calculations were performed for the periodically distributed cavities and cavities with media in frequency domain and the influences of the cavity shape, spacing and stiffness of media on the vibration-isolating effect were discussed.The numerical results show that the displacement amplitude in the case of periodically distributed cavities is different from that in the case of multiple cavities, and the difference is significant at low frequency, indicating that it is difficult to obtain accurate solutions by truncating a finite number of cavities.Among three kinds of shaped cavities, the periodically distributed circular cavities have the best vibration-isolating effect, and the periodically distributed triangular cavities have the worst.The principle of periodically distributed cavities is different from that of periodically distributed cavities with media, the later consumes the energy of seismic waves to reduce earthquake effect, while the former blocks seismic waves to reduce earthquake.The vibration-isolating effect of periodically distributed cavities with flexible media is better than that of periodically distributed cavities with rigid media.

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periodically distributed heterogeneous bodies / Green’s functions / P-waves and SV-waves / scattering and diffraction

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BA Zhenning1,2,GAO Xu1,LIANG Jianwen1,2. Two-dimensional scattering of elastic waves by periodic distribution irregularities in an elastic full space[J]. Journal of Vibration and Shock, 2020, 39(14): 201-213

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