The Inverse Fundamental Operator Marching Method for Cauchy Problems in Range-Dependent Stratified Waveguides

The inverse fundamental operator marching method (IFOMM) is suggested to solve Cauchy problems associated with the Helmholtz equation in stratified waveguides. It is observed that the method for large-scale Cauchy problems is computationally efficient, highly accurate, and stable with respect to the noise in the data for the propagating part of a starting field. In further, the application scope of the IFOMM is discussed through providing an error estimation for the method. The estimation indicates that the IFOMM particularly suits to compute wave propagation in long-range and slowly varying stratified waveguides

Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation

We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation. We prove the well-posedness of the direct problem and obtain a stability estimate of its solution. We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration. Comparative analysis of these methods is presented

Structure Borne Noise Analysis Using Helmholtz Equation Least Squares Based Forced Vibro Acoustic Components

This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction. The technology developed here provides a strategy towards identifying the critical vibration components and methodically suppressing them to achieve a cost-effective noise reduction. The core of this technology is Helmholtz equation least squares (HELS) based nearfield acoustic holography method. In this study, the HELS formulations derived in spherical co-ordinates using spherical wave expansion functions utilize the input data of acoustic pressures measured in the nearfield of a vibrating object to reconstruct the vibro-acoustic responses on the source surface and acoustic quantities in the far field. Using these formulations, three steps were taken to achieve the goal. First, hybrid regularization techniques were developed to improve the reconstruction accuracy of normal surface velocity of the original HELS method. Second, correlations between the surface vibro-acoustic responses and acoustic radiation were factorized using singular value decomposition to obtain orthogonal basis known here as the forced vibro-acoustic components (F-VACs). The F-VACs enables one to identify the critical vibration components for sound radiation in a similar manner that modal decomposition identifies the critical natural modes in a structural vibration. Finally, the dominant F-VAC responsible for acoustic radiation are decomposed into the natural modes of a vibrating structure, and the critical vibration modes responsible for the dominant F-VAC are identified. Experimental validation for this technology was conducted using a baffled square plate and a scaled model vehicle cabin subject to a point force excitation inside a fully anechoic chamber

Holography

This book depicts some differences from the typical scientific and technological literature on the theoretical study of holography and its applications. It offers topics that are not very commercial nor known, which will allow a different view of the field of optics. This is evident in chapters such as "Electron Holography of Magnetic Materials", "Polarization Holographic Gratings in Polymer Dispersed Formed Liquid Crystals", and "Digital Holography: Computer-generated Holograms and Diffractive Optics in Scalar Diffraction Domain". The readers will gain a different view of the application areas of holography and the wide range of possible directions that can guide research in the fields of optics