Computational Wave Field Modeling using Sequential Mapping of Poly-Crepitus Green’s Function in Anisotropic Media

In this thesis, a meshless semi-analytical computational method is presented to compute the ultrasonic wave field in the generalized anisotropic material while understanding the physics of wave propagation in detail. To understand the wave-damage interaction in an anisotropic material, it is neither feasible nor cost-effective to perform multiple experiments in the laboratory. Hence, recently the computational nondestructive evaluation (CNDE) received much attention to performing the NDE experiments in a virtual environment. In this thesis, a fundamental framework is constructed to perform the CNDE experiment of a thick composite specimen in a Pulse-Echo (PE) mode. To achieve the target, the following processes were proposed. The solution of the elastodynamic Green’s function at a spatial point in an anisotropic media was first obtained by solving the fundamental elastodynamic equation using Radon transform and spectral resolution theorem. Next, the basic concepts of wave propagation behavior in a generalized material and the visualization of the anisotropic bulk wave modes were accomplished by solving the Christoffel’s Equation in 3D. Moreover, the displacement and stress Green’s functions in a generalized anisotropic material were calculated in the frequency domain. Frequency domain Green’s functions were achieved by superposing the effect of propagating eigen wave modes that were obtained from the Christoffel’s solution and integrated over the all possible directions of wave propagation by discretizing a sphere. A MATLAB code was developed to compute the displacement and stress Green\u27s functions numerically. Further, the numerically calculated Green’s functions were implemented and integrated with the meshless Distributed Point Source Method (DPSM). DPSM technique was used to virtually simulate a PE NDE experiments of a half-space anisotropic material, inspected by a circular transducer immersed in the fluid. The ultrasonic wave fields were calculated using DPSM after applying the boundary conditions and solving the unknown source strengths. A method named sequential mapping of poly-crepitus Green’s function was introduced and executed along with discretization angle optimization for the time-efficient computation of the wave fields. The full displacements and stress wave fields in transversely isotropic, fully orthotropic and monoclinic materials are presented in this thesis on different planes of the material

Existence and Uniqueness Results for Nonlinear Boundary Value Problems of Elliptic P.D.Es

In my research project I review some elementary application of fixed point principles to prove existence and uniqueness of results for solutions of boundary value problems of ordinary and partial differential equations. The approach is based on the Lp space theory of certain linear differential operators subjected to certain boundary constraints

Computational Wave Field Modeling in Anisotropic Media

In this thesis, a meshless semi-analytical computational method is presented to compute the ultrasonic wave field in generalized anisotropic material while understanding the physics of wave propagation in detail. To understand the wave-damage interaction in an anisotropic material, it is neither feasible nor cost-effective to perform multiple experiments in the laboratory. Hence, recently the computational nondestructive evaluation (CNDE) received much attention to performing the NDE experiments in a virtual environment. In this thesis, a fundamental framework is constructed to perform the CNDE experiment of a thick composite specimen in a Pulse-Echo (PE) and through-transmission mode. To achieve the target, the following processes were proposed. The solution of the elastodynamic Green’s function at a spatial point in an anisotropic media was first obtained by solving the fundamental elastodynamic equation using Radon transform and Fourier transform. Next, the basic concepts of wave propagation behavior in a generalized material and the visualization of the anisotropic bulk wave modes were accomplished by solving the Christoffel’s Equation in 3D. Moreover, the displacement and stress Green’s functions in a generalized anisotropic material were calculated in the frequency domain. Frequency domain Green’s functions were achieved by superposing the effect of propagating eigen wave modes that were obtained from the Christoffel’s solution and integrated over the all possible directions of wave propagation by discretizing a sphere. MATLAB and C++ codes were developed to compute the displacement and stress Green\u27s functions numerically. The generated Green’s function is verified with the existing methodologies reported in the literature. Further, the numerically calculated Green’s functions were implemented and integrated with the meshless Distributed Point Source Method (DPSM). DPSM technique was used to virtually simulate NDE experiments of half-space, 1-layer plate, and multilayered plate anisotropic material for both pristine and damage state scenarios, inspected by a circular transducer immersed in fluid. The ultrasonic wave fields were calculated using DPSM after applying the boundary conditions and solving the unknown source strengths. A method named sequential mapping of poly-crepitus Green’s function was introduced and executed along with discretization angle optimization for the time- efficient computation of the wave fields. The full displacements and stress wave fields in transversely isotropic, fully orthotropic and monoclinic materials are presented in this thesis on different planes of the material. The time domain signal was generated for 1-ply plate at any given point for transversely isotropic, fully orthotropic and monoclinic materials. Finally, the wave field is presented for structures with damage scenarios such as material degradation and delamination and compared with pristine counterparts to visualize and understand the effect of damages/defect in material state

A portable phonatory feedback device for patients with speech disorders

Vocal intensity-related speech disorders such as dysarthria and vocal nodules can limit quality of life and reduce the patient’s ability to interact with family, socialize, or pursue employment. Behavioral speech therapies exist to address these issues but have limited effectiveness because they are expensive and clinic-based. The ability to monitor vocal intensity outside of the clinical setting will greatly aid in the treatment of these speech disorders, enabling patients to make quicker progress by reinforcing techniques learned in the clinic. The Voice Volume Monitor (VVM) is a portable and cost-effective therapeutic aid designed for this purpose, providing real-time feedback regarding speech volume to the user. Initial testing of a prototype with patients at the Our Lady of the Lake Voice Center has shown positive results

A Numerical Study of High Temperature and High Velocity Gaseous Hydrogen Flow in a Cooling Channel of a NTR Core

Two mathematical models (a one and a three-dimensional) were adopted to study, numerically, the thermal hydrodynamic behavior of flow inside a single cooling channel of a Nuclear Thermal Rocket (NTR) engine. The first model assumes the flow in the cooling channel to be one-dimensional, unsteady, compressible, turbulent, and subsonic. The working fluid (GH2) is assumed to be compressible. The governing equations of the 1-D model are discretized using a second order accurate finite difference scheme. Also, a commercial CFD code is used to study the same problem. Numerical experiments, using both codes, simulated the flow and heat transfer in a cooling channel of the reactor. The steady state predictions of both models were compared to the existing experimental results and it is concluded that both models successfully predict the steady state fluid temperature distribution in the NTR cooling channel