Singular Integral Solutions of Analytical Surface Wave Model with Internal Crack

In this study, singular integral solutions were studied to investigate scattering of Rayleigh waves by subsurface cracks. Defining a wave scattering model by objects, such as cracks, still can be quite a challenge. The model’s analytical solution uses five different numerical integration methods: (1) the Gauss–Legendre quadrature, (2) the Gauss–Chebyshev quadrature, (3) the Gauss–Jacobi quadrature, (4) the Gauss–Hermite quadrature and (5) the Gauss–Laguerre quadrature. The study also provides an efficient dynamic finite element analysis to demonstrate the viability of the wave scattering model with an optimized model configuration for wave separation. The obtained analytical solutions are verified with displacement variation curves from the computational simulation by defining the correlation of the results. A novel, verified model, is proposed to provide variations in the backward and forward scattered surface wave displacements calculated by different frequencies and geometrical crack parameters. The analytical model can be solved by the Gauss–Legendre quadrature method, which shows the significantly correlated displacement variation with the FE simulation result. Ultimately, the reliable analytic model can provide an efficient approach to solving the parametric relationship of wave scattering.

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CHARACTERIZATION OF METALLIC NANO-PARTICLES VIA SURFACE WAVE SCATTERING: A. THEORETICAL FRAMEWORK AND FORMULATION

Proceeding of the 4th International Symposium on Radiative Transfer ◽

10.1615/ichmt.2004.rad-4.240 ◽

2004 ◽

Author(s):

Gorden Videen ◽

Mustafa M. Aslan ◽

M. Pinar Menguc

Keyword(s):

Surface Wave ◽

Wave Scattering ◽

Theoretical Framework ◽

Nano Particles

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Effects of Loading and Boundary Conditions on the Performance of Ultrasound Compressional Viscoelastography: A Computational Simulation Study to Guide Experimental Design

Materials ◽

10.3390/ma14102590 ◽

2021 ◽

Vol 14 (10) ◽

pp. 2590

Author(s):

Che-Yu Lin ◽

Ke-Vin Chang

Keyword(s):

Boundary Conditions ◽

Simulation Study ◽

Viscoelastic Properties ◽

Measurement Accuracy ◽

Computational Simulation ◽

Vertical Direction ◽

Fixation Method ◽

Element Analysis ◽

Sample Container

Most biomaterials and tissues are viscoelastic; thus, evaluating viscoelastic properties is important for numerous biomedical applications. Compressional viscoelastography is an ultrasound imaging technique used for measuring the viscoelastic properties of biomaterials and tissues. It analyzes the creep behavior of a material under an external mechanical compression. The aim of this study is to use finite element analysis to investigate how loading conditions (the distribution of the applied compressional pressure on the surface of the sample) and boundary conditions (the fixation method used to stabilize the sample) can affect the measurement accuracy of compressional viscoelastography. The results show that loading and boundary conditions in computational simulations of compressional viscoelastography can severely affect the measurement accuracy of the viscoelastic properties of materials. The measurement can only be accurate if the compressional pressure is exerted on the entire top surface of the sample, as well as if the bottom of the sample is fixed only along the vertical direction. These findings imply that, in an experimental validation study, the phantom design should take into account that the surface area of the pressure plate must be equal to or larger than that of the top surface of the sample, and the sample should be placed directly on the testing platform without any fixation (such as a sample container). The findings indicate that when applying compressional viscoelastography to real tissues in vivo, consideration should be given to the representative loading and boundary conditions. The findings of the present simulation study will provide a reference for experimental phantom designs regarding loading and boundary conditions, as well as guidance towards validating the experimental results of compressional viscoelastography.

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