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Surface irregularities on the earth, such as hills and ridges, can amplify the ground motion caused by earthquakes and cause damage to buildings. Hence, it is crucial to study the ground motion amplification on hills and their environs under the effect of earthquakes. In this research, the seismic response of a triangular rocky hill subject to cylindrical horizontally polarized shear (SH) waves is investigated by means of a boundary integral equation method. A comparison is made to verify the feasibility of the present method. Parametric studies are performed to evaluate the influences of source location and hill shape on the ground accelerations on the hill and its environs under cylindrical SH waves of different frequencies. The results show that the ground accelerations near the hill are strongly relative to the source location. For a near-source scattering problem, the cylindrical wavefront assumption is more appropriate than the plane wave assumption. The thinner hill is more likely to cause multiple reflections of the seismic waves inside it, resulting in a stronger ground motion near the hillcrest. The acceleration response spectrum at the hillcrest is amplified in a wide period range of 0–4 s, and increasing the hill height will strengthen the amplification effect. The presence of the hill also results in the amplification of the acceleration response spectrum in the period range of 0–0.7 s on the flat ground surface.HighlightsThe seismic response of a triangular hill to cylindrical SH waves was investigated.Necessity of cylindrical wavefront assumption for near-source problem was verified.Mechanism of ground motion amplification on a triangular hill was revealed.

In this paper, the shear horizontal (SH) wave scattering by a circular pipeline in an inhomogeneous concrete with density variation is studied. A model of inhomogeneous concrete with density variation in the form of a polynomial-exponential coupling function is established. By using the complex function method and conformal transformation, the incident and scattering wave field of SH wave in concrete are obtained, and the analytic expression of dynamic stress concentration factor (DSCF) around the circular pipeline is given. The results show that the inhomogeneous density parameters, the wave number of the incident wave and the angle of the incident wave in concrete are important factors affecting the distribution of dynamic stress around the circular pipe in concrete with inhomogeneous density. The research results can provide a theoretical reference and a basis for analyzing the influence of circular pipeline on elastic wave propagation in an inhomogeneous concrete with density variation.

In this paper, a square mass oscillator elastic metasurface (SMEM) is used to manipulate flexural wave and SH wave. Due to the symmetry of its oscillator in z and y directions, the functional units of the SMEM have the same phase delay effects in the motion direction of the two waves, so as to realize the modulation of flexural and SH waves. According to Generalized Snell’s Law, abnormal refraction and beam focusing can be achieved by reasonably changing the side length of the cross section. In particular, the proposed metasurface can even realize the abnormal refraction of two waves simultaneously. In addition, the multiple mass oscillator array design (MMAD) can also greatly broaden the operating frequency domain. This study presents a method for achieving multifunctional metasurfaces with potential applications in areas such as vibration control, energy harvesting, and noise isolation.

This study addresses the dynamic behavior of a circular tunnel in inhomogeneous multi-layer soil structures with complex boundary conditions. First, we consider two types of inhomogeneous density: density varies with the square term of coordinates, and density varies with the exponential term of coordinates. By introducing new variables, the variable coefficient Helmholtz equation is transformed into standard form. Then, SH wave is considered as a seismic wave acting on multi-layer soil structures. On the basis of series expansion method, the analytical expression of scattering wave in each soil layer is conducted, and the analytical expression of standing wave is established, which satisfies the stress-free conditions on the boundaries of V-shaped canyon by the fractional Bessel function expansion method and Graf addition theorem. Finally, large-arc assume method is applied, the multi-layer soil structures are divided into three parts along the horizontal interface, the straight boundaries are converted into curved boundaries, and the expressions of scattering waves caused by curved boundaries are obtained. The integral equations are set up through boundary conditions and solved by applying orthogonal function expansion technique and effective truncation. The calculation results analyzed and discussed the dynamic stress concentration factor of tunnel in different soil layers. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.

Previous studies mostly used plane waves as the source input to study the influence of topography effects without considering the source distance. However, the influence of source effect on topography amplification cannot be ignored. This study presents a series solution for the scattering of cylindrical SH waves by a shallow asymmetric V-shaped canyon, and the effect of the location of the source on the topography magnification is investigated. The presented formulations in this paper first divide the asymmetric shallow V-shaped canyon into enclosed and open regions using the region-matching method. The free wavefield of cylindrical SH wave is solved by the image theory, and the wavefield in the enclosed and open regions is obtained based on the separation of variable method. The Graf’s formula is derived to unify the wavefield coordinates of the two regions, and the unknown coefficients of the wavefield are solved by the continuity condition of the boundary. Then, the proposed solution is verified by comparisons with published data for two cases (e.g. those pertaining to the symmetrical V-shaped canyon of cylindrical SH waves and the asymmetric shallow V-shaped canyon of plane SH waves). Finally, the effect of the source position, the width, and the dimensionless frequency of the asymmetric V-shaped canyon on the surface displacement amplification is discussed. It is found that the difference of displacement amplitude between asymmetric canyon and symmetric canyon can reach 270.2% under the cylindrical SH waves, that is, the asymmetric effect of the canyon has a significant influence on the topography amplification. The cylindrical SH waves cannot simply be regarded as plane SH waves unless the source location r 0 exceeds 100 times canyon depth and it is necessary to use cylindrical SH waves to simulate the influence of near-source effects on topography amplification when the source is relatively close. Therefore, the near-source effect should warrant careful engineering attention in the seismic design of large-span structures such as bridges across shallow V-shaped canyons.

Surface irregularities, such as hills and ridges, can significantly amplify ground motion caused by earthquakes. Therefore, in this study, we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves. Firstly, based on the development of wave functions and regional matching techniques, we introduce a semi-circular artificial auxiliary boundary, dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region. Secondly, we derive the domain function form applicable to solving asymmetric problems. Utilizing the theory of complex variables, we establish a well-posed matrix for solving domain functions within the same coordinate system. Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence. Additionally, the frequency of the incident wave also has a certain degree of impact on the displacement amplitude. This study elucidates the scattering mechanism of SH waves by complex boundaries, providing a theoretical reference for building site selection and seismic design. In practical problems, the asymmetric assumption is more applicable than the symmetry assumption.

The discontinuity of the medium and the irregularity of the ground significantly affect the propagation of seismic waves. However, the comprehensive effects of these two factors on seismic motion have not yet been fully investigated. To reveal the mechanism of dynamic interaction between the discontinuity and the irregular topography, this study provides a series of solution for the scattering of plane SH waves caused by a concentric semi-cylindrical discontinuity and canyon in an elastic half-space, using the displacement discontinuity model and the wave function expansion method. Based on the proposed series solution, a systematic analysis is conducted to investigate the influences of the stiffness of the discontinuity, the radius ratio between the discontinuity and the canyon, and the properties (e.g., frequency and angle) of the incident wave on the ground motion and underground motion. The results indicate that the stiffness of the discontinuity is a key factor determining the distribution of seismic motion. A high stiffness leads to a distribution similar to that of the canyon alone, while a low stiffness results in a much more complex distribution.

This study analytically investigates shear horizontal (SH) wave propagation in a layered structure consisting of a piezoflexoelectric (PFE) layer bonded to an elastic substrate, considering an imperfect interface. A frequency equation is derived by applying appropriate boundary and interfacial conditions, capturing the effects of flexoelectric coupling, interface imperfections, the layer thickness, and the material properties. The resulting dispersion relation reveals that both interface imperfections and the flexoelectric strength significantly alter the phase velocity of SH waves. Numerical simulations show that increasing flexoelectric coefficients or interface imperfections lead to notable changes in dispersion behavior. Comparative analyses under electrically open (EO)- and electrically short (ES)-circuited boundary conditions demonstrate their impacts on wave propagation. These findings offer new insights into the design and analysis of piezoflexoelectric devices with realistic interface conditions.

The propagation of nonlinear shear horizontal (SH) waves in an incompressible hyper-elastic plate of uniform thickness is investigated. It is assumed that the plate is made of heterogeneous, isotropic, and generalized neo-Hookean materials. By applying the method of multiple scales, a nonlinear Schrödinger (NLS) equation is derived describing the nonlinear self modulation of the waves. As a result of known solutions of an NLS equation, it is found that the antisymmetric bright solitary SH waves will exist and propagate in this plate. Moreover, not only the effect of the heterogeneity but also the effect of the nonlinearity on the deformation field is discussed for these waves.

A novel analytical solution for stresses and displacements of deep tunnels near a fault zone subjected to SH waves is presented. The ground, fault and liner are assumed as linear isotropic elastic, with a no-slip condition at all contact interfaces. It is assumed that the tunnel is parallel to the fault and therefore the displacements perpendicular to the tunnel axis are zero. The effect of the fault on the wave diffracted by the tunnel is neglected, to be able to obtain the solution. Validation of the proposed analytical solution is accomplished by comparing the results of the solution with those obtained from ABAQUS. The relevance of key parameters, namely: the stiffness ratio between the fault and the ground, the width of the fault, and the frequency of the incident SH wave, are discussed using the numerical results and analytical formulation.HighlightsAnalytical solution for response of deep tunnels near a fault zone subjected SH waves is proposed.Simple formulations are given to obtain the maximum effect of faults on seismic response of tunnels.Results show significant impacts of the width of the fault on tunnel seismic performances.The presented solution could be an effective and efficient tool for practitioners.