Dynamic Response of Deep V-Shaped Slopes for Incident SH Waves
- 1The College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
- 2China Earthquake Disaster Prevention Center, Beijing 100029, China
Abstract
It is essential to explore dynamic response of a deep V-shaped slope for incident SH waves, meeting the challenges of extreme disasters including earthquakes. A novel analytical solution is proposed to effectively evaluate dynamic response of deep V-shaped slopes for incident SH waves. A validation of this solution is confirmed through comparisons with boundary integral equations and another analytical approach. More importantly, it can provide the exact analytical expressions of unknown coefficients of wave functions and present a new idea solving relative problems. The new numerical results show that displacement amplitudes and phases change apparently with the dimensionless distance. Moreover, effects of incident angles, angles of slopes and the dimensionless frequencies to the dynamic response of deep V-shaped slopes are significantly discussed in a wide range of frequencies. Regular patterns of displacement amplitudes are symmetric for vertical incidence. The oscillation numbers of displacement amplitudes on a facing wave surface and its left are often more than these on a shadow surface and its right for oblique and horizontal incidence. However, the regular patterns of displacement phases versus the dimensionless distance are similar. This study would enhance theoretical and practical significance for an analytical approach, wave motion and site effects.
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BibTeX
@article{ren2026dynamic,
title = {{Dynamic Response of Deep V-Shaped Slopes for Incident SH Waves}},
author = {Peng Ren and Fuchu Dai and Sanhong Chen},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203792},
url = {https://www.mdpi.com/2227-7390/14/20/3792},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Dynamic Response of Deep V-Shaped Slopes for Incident SH Waves
AU - Peng Ren
AU - Fuchu Dai
AU - Sanhong Chen
PY - 2026
DA - 2026/10/19
JO - Mathematics
DO - 10.3390/math14203792
UR - https://www.mdpi.com/2227-7390/14/20/3792
AB - It is essential to explore dynamic response of a deep V-shaped slope for incident SH waves, meeting the challenges of extreme disasters including earthquakes. A novel analytical solution is proposed to effectively evaluate dynamic response of deep V-shaped slopes for incident SH waves. A validation of this solution is confirmed through comparisons with boundary integral equations and another analytical approach. More importantly, it can provide the exact analytical expressions of unknown coefficients of wave functions and present a new idea solving relative problems. The new numerical results show that displacement amplitudes and phases change apparently with the dimensionless distance. Moreover, effects of incident angles, angles of slopes and the dimensionless frequencies to the dynamic response of deep V-shaped slopes are significantly discussed in a wide range of frequencies. Regular patterns of displacement amplitudes are symmetric for vertical incidence. The oscillation numbers of displacement amplitudes on a facing wave surface and its left are often more than these on a shadow surface and its right for oblique and horizontal incidence. However, the regular patterns of displacement phases versus the dimensionless distance are similar. This study would enhance theoretical and practical significance for an analytical approach, wave motion and site effects.
SN - 2227-7390
ER -