“…e top side radius of the isosceles trapezoid is set to L 3 � 0.5. e bottom side radius of the isosceles trapezoid is set to L 4 � 1, and the incident angles are 0 o , 30 o , 60 o , and 90 o . As shown in Figure 4, the computation result of the complex landforms model reducing the isosceles trapezoid is nearly the same as the literature [21]. e abovementioned reducing model computation confirms the accuracy and applicability of the method in this article.…”
Section: Numerical Calculation and Analysissupporting
confidence: 79%
“…As is shown in Figure 3, the computation result of the complex landforms model reducing semicircular depression is nearly the same as the literature [9]. Finally, the complex landforms model is reduced to only contain the isosceles trapezoid hill, and the isosceles trapezoid hill size data is set according to the literature [21]. e top side radius of the isosceles trapezoid is set to L 3 � 0.5. e bottom side radius of the isosceles trapezoid is set to L 4 � 1, and the incident angles are 0 o , 30 o , 60 o , and 90 o .…”
Section: Numerical Calculation and Analysismentioning
confidence: 72%
“…e corresponding expressions for ξ (ℓ) m , ζ (k) m , l � 11, 12,13,14,21,22,23,24,32,33,34,35,36,42,43,44,45,46,55,56,57,65,66,67,72,73,74, k � 1, 2, 3, 4, 5, 6, 7 in equation ( 58) are shown as follows.…”
Section: Appendixmentioning
confidence: 99%
“…Wang [20] studied the seismic response of a tunnel lining structure embedded in a thick expansive soil stratum. Shyu [21] proposed a novel strategy for the investigation of displacement amplitude near and along symmetric dikes comprising a trapezoidal structure with a circular-arc foundation when subjected to SH waves.…”
The multiple scattering of SH waves by isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill in the solid half-space is studied. The complex model is divided into multiple subdomains by using the region matching method, then the wave functions in each subdomain are constructed by using the fractional-order Bessel function, and finally, the infinite algebraic equations for solving the unknown coefficients in the wave function are established by using the multipolar coordinate technique and the complex function method according to the boundary conditions. Fourier series is used to solve the unknown undetermined coefficients. The results show that due to the multiple reflections of the incident wave between complex landforms, surface displacement amplitude is affected by the incident angle, incident frequency, and the distance between the isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill. It is found that when the incident frequency increases, there is a certain amplification effect between the hills and the depression. When the wave is incident horizontally, there is a certain “barrier” effect between hills and depression, and when the distance between the hills and depression reaches a certain level, the “barrier” effect will reach a stable value.
“…e top side radius of the isosceles trapezoid is set to L 3 � 0.5. e bottom side radius of the isosceles trapezoid is set to L 4 � 1, and the incident angles are 0 o , 30 o , 60 o , and 90 o . As shown in Figure 4, the computation result of the complex landforms model reducing the isosceles trapezoid is nearly the same as the literature [21]. e abovementioned reducing model computation confirms the accuracy and applicability of the method in this article.…”
Section: Numerical Calculation and Analysissupporting
confidence: 79%
“…As is shown in Figure 3, the computation result of the complex landforms model reducing semicircular depression is nearly the same as the literature [9]. Finally, the complex landforms model is reduced to only contain the isosceles trapezoid hill, and the isosceles trapezoid hill size data is set according to the literature [21]. e top side radius of the isosceles trapezoid is set to L 3 � 0.5. e bottom side radius of the isosceles trapezoid is set to L 4 � 1, and the incident angles are 0 o , 30 o , 60 o , and 90 o .…”
Section: Numerical Calculation and Analysismentioning
confidence: 72%
“…e corresponding expressions for ξ (ℓ) m , ζ (k) m , l � 11, 12,13,14,21,22,23,24,32,33,34,35,36,42,43,44,45,46,55,56,57,65,66,67,72,73,74, k � 1, 2, 3, 4, 5, 6, 7 in equation ( 58) are shown as follows.…”
Section: Appendixmentioning
confidence: 99%
“…Wang [20] studied the seismic response of a tunnel lining structure embedded in a thick expansive soil stratum. Shyu [21] proposed a novel strategy for the investigation of displacement amplitude near and along symmetric dikes comprising a trapezoidal structure with a circular-arc foundation when subjected to SH waves.…”
The multiple scattering of SH waves by isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill in the solid half-space is studied. The complex model is divided into multiple subdomains by using the region matching method, then the wave functions in each subdomain are constructed by using the fractional-order Bessel function, and finally, the infinite algebraic equations for solving the unknown coefficients in the wave function are established by using the multipolar coordinate technique and the complex function method according to the boundary conditions. Fourier series is used to solve the unknown undetermined coefficients. The results show that due to the multiple reflections of the incident wave between complex landforms, surface displacement amplitude is affected by the incident angle, incident frequency, and the distance between the isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill. It is found that when the incident frequency increases, there is a certain amplification effect between the hills and the depression. When the wave is incident horizontally, there is a certain “barrier” effect between hills and depression, and when the distance between the hills and depression reaches a certain level, the “barrier” effect will reach a stable value.
“…On the other hand, results from other researches in basin acoustics are applicable to this problem; for waves in an empty and triangular canyon, the displacement transfer function was revealed to be 0.5–1.5 within the canyon 15 . Another study in which waves near a dike were modeled demonstrated that the transfer function value to be approximately 10 at the top of the dike 16 . This value was larger than in our experiment (5.3) because the larger value was calculated near the resonant frequency.…”
The eye orbit has mechanical and acoustic characteristics that determine resonant frequencies and amplify acoustic signals in certain frequency ranges. These characteristics also interfere with the acoustic amplitudes and frequencies of eyeball when measured with an acoustic tonometer. A model in which a porcine eyeball was embedded in ultrasonic conductive gel in the orbit of a model skull was used to simulate an in vivo environment, and the acoustic responses of eyeballs were detected. The triggering source was a low-power acoustic speaker contacting the occipital bone, and the detector was a high-resolution microphone with a dish detecting the acoustic signals without contacting the cornea. Dozens of ex vivo porcine eyeballs were tested at various intraocular pressure levels to detect their resonant frequencies and acoustic amplitudes in their power spectra. We confirmed that the eyeballs’ resonant frequencies were proportional to intraocular pressure, but interference from orbit effects decreased the amplitudes in these resonant frequency ranges. However, we observed that the frequency amplitudes of eyeballs were correlated with intraocular pressure in other frequency ranges. We investigated eye orbit effects and demonstrated how they interfere with the eyeball’s resonant frequencies and frequency amplitudes. These results are useful for developing advanced acoustic tonometer.
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