The theory of electromagnetic characteristic modes was published roughly forty years ago, for both conducting and penetrable objects. However, while the characteristic mode analysis of conducting objects has found renewed interest as a tool for antenna designers, computed results for the characteristic mode eigenvalues, eigencurrents and eigenfields for penetrable objects have not appeared, not even in the seminal papers on the subject. In this thesis both volume and surface integral equation formulations are used to compute the characteristic modes of penetrable objects for what appears to be the first time. This opens the way for the use of characteristic mode theory in the design of antennas made of penetrable material whose polarization current densities constitute the main radiating mechanism of the antenna. Volume formulations are shown to be reliable but computationally burdensome. It is demonstrated that surface formulations are computationally more efficient, but obtrude some non-physical modes in addition to the physical ones. Fortunately, certain field orthogonality checklists can be used to provide a straightforward means of unambiguously selecting only the physical modes. The sub-structure characteristic mode concept is extended to problems involving both perfectly conducting and penetrable materials. It is also argued that sub-structure modes can be viewed as characteristic modes that implicitly use modified Green’s functions, but without such Green’s functions being needed explicitly. This makes the concept really practical, since the desired modified Green’s functions are not known explicitly in most cases.

The theory of electromagnetic characteristic modes was published roughly forty years ago, for both conducting and penetrable objects. However, while the characteristic mode analysis of conducting objects has found renewed interest as a tool for antenna designers, computed results for the characteristic mode eigenvalues, eigencurrents and eigenfields for penetrable objects have not appeared, not even in the seminal papers on the subject. In this thesis both volume and surface integral equation formulations are used to compute the characteristic modes of penetrable objects for what appears to be the first time. This opens the way for the use of characteristic mode theory in the design of antennas made of penetrable material whose polarization current densities constitute the main radiating mechanism of the antenna. Volume formulations are shown to be reliable but computationally burdensome. It is demonstrated that surface formulations are computationally more efficient, but obtrude some non-physical modes in addition to the physical ones. Fortunately, certain field orthogonality checklists can be used to provide a straightforward means of unambiguously selecting only the physical modes. The sub-structure characteristic mode concept is extended to problems involving both perfectly conducting and penetrable materials. It is also argued that sub-structure modes can be viewed as characteristic modes that implicitly use modified Green’s functions, but without such Green’s functions being needed explicitly. This makes the concept really practical, since the desired modified Green’s functions are not known explicitly in most cases.

Current dynamic testing methods can prove unrealistic due to the scale at which test components are modelled, the rate at which they are loaded or the boundary conditions to which they are subjected. A new test method, termed "Real-Time Sub-Structure Testing" seeks to provide a more realistic testing environment for energy dissipative components. The method tests structural components at full or large scale and in real-time. The physical test interacts with a computer model of the structure surrounding the test component. In this way, the in-situ behaviour of the test component is evaluated in relation to the overall structural response. The testing method requires fast and realistic modelling of the surrounding structure and a rapid interaction with the physical test specimen. For these reasons, a new non-linear finite element method has been proposed in order to model the surrounding structure behaviour efficiently. The method uses the Central Difference Method time stepping integration scheme together with a newly devised basis. The proposed basis consists of the structure’s elastic modes and additional Ritz vectors, which are calculated from the inelastic static displacement shapes of the structure. The displacement shapes correspond to the same static spatial distribution of loading as the intended dynamic excitation, and are intended to characterise the inelastic behaviour of the structure. The method has been validated against a Newmark event to event algorithm as well as Drain2DX. The non-linear dynamic response of a propped cantilever beam and portal frame structure was investigated. The response evaluated by the algorithm agrees closely with both validation analyses. The new algorithm was also shown to be faster than the Newmark procedure in simple benchmark tests. In addition, a numerical model of the testing apparatus has been developed in order to simulate complete tests for the purposes of testing procedure development and validation. The model is developed using Matlab Simulink. Parameters for the model are deduced from published data, experimental component tests and open loop step response calibrations. The model behaviour was found to be very sensitive to the parameters used. However, after calibration against open loop tests the model reproduces the observed laboratory behaviour to a good degree of accuracy. In an attempt to predict the behaviour of an actual test, the laboratory model has been coupled with the new structural solution algorithm to simulate a virtual test. The simulated results compare well with experimentally observed data demonstrating the usefulness of the overall simulation as a test modelling tool.

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The Theory of Characteristic Modes is being adopted by many research groups around the world in the last decade. This topic and their use in different metallic antenna design is growing very fast. However, most of the applications has been only concentrated on conducting surfaces without any physical knowledge about its limitations and its physical interpretation. As far as dielectric bodies are concerned, there have not been so many published articles. The reason is that there are different integro-differential formulations and the interpretation of their solutions is not as obvious as in conducting bodies. Here, a theoretical interpretation considering loss-less conducting and dielectric bodies is presented. The conclusions drawn in this thesis will allow us to better understand the solutions of the Theory of Characteristic Modes and their limitations. This is important for antenna engineering. In addition, this analysis will allow to develop a novel method for the design of antennas based on dielectric resonators, DRA. This method is called Substructure based-PMCHWT method, and is based on the implementation of the Schur complements of the method of moments matrix operator. This study permits to optimize the radiation bandwidth in the same analysis process for both, the dielectric and the feed, e.g. slot. Moreover, it allows to understand how the slot behaves in the presence of the dielectric resonator and vice versa. This method can also be used to design DRA using low permittivities. This is important in the design of DRA because the feed perturbs the system and produces a shift in the resonances of the characteristic modes. So, therefore, by considering the feed system in the characteristic modes analysis a more realistic results than a conventional analysis is obtained. On the other hand, the resonances of the characteristic modes at low permittivities are displaced from what are the natural resonances of the dielectric resonator and also the corresponding S11 resonance. Thus, designing with this new method it can draw new conclusions about the design of DRA using the Theory of Characteristic Modes. / En la última década, la teoría de los modos característicos está siendo utilizada por muchos grupos de investigación en todo el mundo. Este tema y su uso en diferentes diseños de antenas metálicas está creciendo muy rápido. Sin embargo, la mayoría de las aplicaciones se han concentrado únicamente en antenas metálicas sin ningún conocimiento físico acerca de sus limitaciones y su interpretación física. En lo que se refiere a cuerpos dieléctricos, no han habido tantos artículos publicados como en metales. La razón es que existen diferentes formulaciones integro-diferenciales y la interpretación de sus soluciones no es tan obvia como en cuerpos metálicos. En esta tesis se presenta una interpretación física de las soluciones de la Teoría de Modos Característicos al considerar cuerpos metálicos y dieléctricos sin pérdidas. Las conclusiones de esta tesis nos permitirán comprender mejor las soluciones de la Teoría de Modos Característicos y sus limitaciones. Esto es importante en ingeniería de antenas. Además, este análisis permitirá desarrollar un nuevo método para el diseño de antenas basadas en resonadores dieléctricos, DRA. Este método está basado en la formulación PMCHWT y la función de Green multicapa utilizada en el método de los momentos (MoM). A este nuevo método se le ha denominado "Substructure Characteristic Mode method", y está basado en la implementación de los complementos Schur sobre las submatrices del operador del MoM. Este estudio permite optimizar el ancho de banda de radiación de un DRA en el mismo proceso de análisis tanto para el dieléctrico como para la alimentación, como por ejemplo una ranura. Además, este método permite comprender como se comporta la ranura en presencia del resonador dieléctrico y viceversa. Este método también puede usarse para diseñar DRA usando permitividades bajas. Esto es importante en el diseño de DRA porque la alimentación perturba el sistema y produce un cambio en las resonancias de los modos característicos. Por lo tanto, al considerar la alimentación en el análisis de modos característicos se obtienen resultados más realistas comparándolos con los obtenidos mediante un análisis convencional. Así, diseñando con el "Substructure Characteristic Mode method" se pueden extraer nuevas conclusiones sobre el diseño de DRA mediante la Teoría de Modos Característicos. / En l'última dècada, la teoria dels modes característics està sent utilitzada per molts grups d'investigació en tot el món. Este tema i el seu ús en diferents dissenys d'antenes metàl·liques està creixent molt ràpid. No obstant això, la majoria de les aplicacions s'han concentrat únicament en superfícies conductores sense cap coneixement físic sobre les seues limitacions i la seua interpretació física. Pel que fa a cossos dielèctrics, no hi ha hagut tants articles publicats com en metalls. La raó és que hi ha diferents formulacions integro- diferencials i la interpretació de les seues solucions no és tan òbvia com en cossos conductors. En esta tesi es presenta una interpretació teòrica considerant cossos conductors i dielèctrics sense pèrdues. Les conclusions d'esta tesi ens permetran comprendre millor les solucions de la Teoria de Modes Característics i les seues limitacions. Açò és important en enginyeria d'antenes. Açò és important en enginyeria d'antenes. A més, esta anàlisi permetrà desenrotllar un nou mètode per al disseny d'antenes basades en ressonadors dielèctrics, DRA. Este mètode està basat en la formulació PMCHWT i la funció de Green multicapa utilitzada en el mètode dels moments (MoM) . A este nou mètode se li ha denominat "Substructure Characteristic Mode method", i està basat en la implementació dels complements Schur sobre les submatrius de l'operador del MoM. Este estudi permet optimitzar l'amplada de banda de radiació d'un DRA en el mateix procés d'anàlisi tant per al dielèctric com per a l'alimentació, com per exemple una ranura. A més, este mètode permet comprendre com es comporta la ranura en presència del ressonador dielèctric i viceversa. Este mètode també pot usar-se per a dissenyar DRA usant baixes permitivitats. Açò és important en el disseny de DRA perquè l'alimentació pertorba el sistema i produïx un canvi en les ressonàncies dels modes característics. Per tant, al considerar l'alimentació en l'anàlisi de modes característics s'obtenen resultats més realistes comparant-los amb els obtinguts per mitjà d'una anàlisi convencional. Així, dissenyant amb el "Substructure Characteristic Mode method" es poden extraure noves conclusions sobre el disseny de DRA per mitjà de la Teoria de Modes Característics. / Bernabeu Jiménez, T. (2017). Contribution to the physical interpretation of characteristic mode resonances. Application to dielectric resonator antennas [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86177

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.