Surface motion of a semi-elliptical hill for incident plane SH waves

Liang, Jianwen; Fu, Jia

doi:10.1007/s11589-011-0807-1

Cited by 20 publications

(5 citation statements)

References 19 publications

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“…Among the isotropic studies by analytic approaches can name Sabina & Willis (1975) who used the the asymptotic wave function expansion method to provide the initial responses of the hills. Other researchers such as Yuan & Liao (1996), Cao et al (2001), Wang & Liu (2002), Lee et al (2004), Tsaur & Chang (2009), Liang & Fu (2011), Amornwongpaibun & Lee (2013), Zhang et al (2018) and Liu et al (2019) were able to study the hills behavior by analytic methods including the Bessel-Fourier function, the complex variable/function, the wave function expansion, the conformal mapping methods, etc. Moreover, Ohyoshi (1973), Lobanov & Novichkov (1981), Nayfeh & Chimenti (1988), Bao et al (1997), Chen & Liu (2005), Ke (2012), Vinh & Anh (2014), Rajak & Kundu (2019) analytically investigated the waves propagation in an anisotropic as well as orthotropic medium.…”

Section: Literature Surveymentioning

confidence: 99%

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

Mojtabazadeh-Hasanlouei

Panji

Kamalian

2023

Preprint

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A simple numeric model named DASBEM was successfully developed to analyze the seismic heterogeneous orthotropic hill-shaped topographies by a time-domain boundary element method based on half-space Green’s functions. The model was elaborated only by discretizing the hill surface and its interface with the underlying half-space in the use of image source theory and substructure approach. To improve the model at the corners, the double node procedure was applied to extreme nodes of the used quadratic elements. An attenuation ratio is implemented in the boundary equations using a decremental exponential function. After presenting the technique, a validation example presented beside the literature to measure the convergence with an isotropic response. Then, a sample Gaussian–shaped hill model is prepared under propagating obliquely incident SH-waves as common sample topography and the surface response is obtained by considering some significant parameters as well as the shape ratio, isotropy factor, frequency content, and angle of the incident wave. The ground surface response is sensitized in two time and frequency realms. The results showed that the amplitude of the response was not only dependent on the impedance ratio but also the isotropy ratio was always effective in orienting the wavefront to amplify the ground movement.

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Section: Literature Surveymentioning

confidence: 99%

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

Mojtabazadeh-Hasanlouei

Panji

Kamalian

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Among the isotropic studies by analytical approaches can name Sabina & Willis (1975) who used the asymptotic wave function expansion method to provide the initial responses of the hills. Other researchers such as Yuan & Liao (1996), Cao et al (2001), Wang & Liu (2002), Lee et al (2004), Tsaur & Chang (2009), Liang & Fu (2011), Amornwongpaibun & Lee (2013), Zhang et al (2018), Liu et al (2019) and were able to study the hills behavior by analytical methods including the Bessel-Fourier function, the complex variable/function, the wave function expansion, the conformal mapping methods, etc. Moreover, Ohyoshi (1973), Lobanov & Novichkov (1981), Nayfeh & Chimenti (1988), Bao et al (1997), Chen & Liu (2005), Ke (2012), Vinh & Anh (2014), Rajak & Kundu (2019) analytically investigated the waves propagation in an anisotropic as well as orthotropic medium.…”

Section: Literature Reviewmentioning

confidence: 99%

A Simple TD-BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies

Mojtabazadeh-Hasanlouei,

Panji,

Kamalian

2023

Preprint

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A simple numerical model named DASBEM was successfully developed to analyze the seismic heterogeneous orthotropic hill-shaped topographies by a time-domain boundary element method (TD-BEM) based on half-space Green’s functions. The model was elaborated only by discretizing the hill surface and its interface with the underlying half-space in the use of image source theorem and substructure approach. To improve the model at the corners, the double node procedure was applied to extreme nodes of the used quadratic elements. An attenuation ratio is implemented in the boundary equations using a decremental exponential function. After presenting the technique, a validation example presented beside the literature to measure the convergence with an isotropic response. Then, a sample Gaussian–shaped hill model is prepared under propagating obliquely incident SH-waves as common sample topography and the surface response is obtained by considering some significant parameters as well as the shape ratio, isotropy factor, frequency content, and angle of the incident wave. The ground surface response is sensitized in two time and frequency domains. The results showed that the amplitude of the response was not only dependent on the impedance ratio, but also the isotropy ratio was always effective in orienting the wavefront to amplify the ground movement.

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“…In accordance with the principle of wave superposition, the full wave function in the medium can be expressed as

u_{z 1} = {u_{z 1}}^{i} (ξ, η, q_{1}) + {u_{z 1}}^{s} (ξ, η, q_{1})

In addition, the standing wave generated in the elliptical inclusion can be represented as 10

{u_{z}}_{2} = {false\sum}_{m = 0}^{\infty} - D_{m} {italicMc}_{m}^{1} (ξ, q_{2}) {italicce}_{m} (η, q_{2}) + {false\sum}_{m = 1}^{\infty} - E_{m} {italicMs}_{m}^{1} (ξ, q_{2}) {italicse}_{m} (η, q_{2})

In the elliptical coordinate system, the stress component is given by the following formula 25 :

\{\begin{matrix} center \\ σ_{ξ} = \frac{μ}{italicaJ} \frac{\partial u_{z}}{\partial ξ} \\ σ_{η} = \frac{μ}{italicaJ} \frac{\partial u_{z}}{\partial η} \end{matrix}

The undetermined coefficient can be determined by applying the boundary conditions. The boundary conditions require continuity of the displacement and stress along the inclusion surface, which can be expressed as

\{\begin{matrix} center \\ u_{z 1} (ξ_{0}, η, q_{1}) = u_{z 2} (ξ_{0}, η, q_{2}) \\ σ_{ξz 1} () \end{matrix}

…”

Section: Steady‐state Response Of Inclusionmentioning

confidence: 99%

Dynamic analysis of the different types of elliptic cylindrical inclusions subjected to plane SH‐wave scattering

Tao

Luo

et al. 2022

Math Methods in App Sciences

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The complex boundary of the elliptical inclusion rendered it difficult to solve the problem of wave scattering. In this study, the steady‐state response was analyzed using the wave function expansion method. Subsequently, the Ricker wavelet was employed as the transient disturbance, and Fourier transform was used to determine the distribution of transient dynamic stress concentration around the elliptical inclusion. The effects of wave number, elliptical axial ratio, and difference in material properties on the distribution of the dynamic stress concentration around the elliptical inclusion were evaluated. The numerical results revealed that the dynamic stress concentration always appeared at both ends of the major axis and minor axis of the elliptical inclusion, and the difference in material properties between the inclusion and medium influenced the variations in the dynamic stress concentration factor with the wave number and elliptical axial ratio.

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Surface motion of a semi-elliptical hill for incident plane SH waves

Cited by 20 publications

References 19 publications

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

A Simple TD-BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies

Dynamic analysis of the different types of elliptic cylindrical inclusions subjected to plane SH‐wave scattering

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