Wave-induced circulation in general coastal environments is simulated by coupling two widely-used finite-element models, namely, a refraction-diffraction-reflection model based on the elliptic mild-slope equation, and a two-dimensional (depth-averaged) shelf-scale circulation model. Such models yield wave-induced current-fields and set-up/down. This involves exploration of some numerical and practical issues, for example, the selection of appropriate boundary condition and grid resolution, numerical errors owing to higher-order derivatives, etc. Computations of the wave forcing from the elliptic wave model, and the wave-induced quantities from the circulation model, are validated with theoretical and published results. The coupled system is then used to simulate the wave-induced circulation in the domains where structures (e.g. breakwater, jetty, etc.) and bathymetric features (e.g. shoal, etc.) are present. In practice, usually an approximate form of the wave-induced forcing is used. This has certain limitations in some application, which have been poorly studied so far. Therefore, here we consider two alternative approaches. The performance of these wave forcing formulations is examined in the regions where the effects of wave reflection, diffraction and focusing are significant. It is observed that the “generalized approach” provides satisfactory results in most situations, provided a grid resolution of L/10 or more is achievable for the wave model domain. The widely-used simplified approach may produce a chaotic pattern of set-up/down and current field in the regions where the wave field is not purely progressive. The third approach ignores the effect of wave diffraction and reflection, and primarily simulates the effect of energy dissipation. Differences up to 25 percent are observed between the modeled current fields obtained with the generalized and the simplified approach. The results suggest that the generalized approach can be used with little practical difficulty and greater reliability.

No description available.

Pile-supported ports allow seawater to run below the deck, and thus may suffer structural damages during extreme coastal events such as hurricanes. These structural damages, in turn, may result to port closures that can cause significant economic losses. Risk analysis can predict the post-hazard functionality of ports though the structural damage assessment of these structures prior to coastal events. However, assumptions on the selected demand estimates may affect the estimated probability of structural damage. This research aims to shed light on the sensitivity of the wave model selection for the risk assessment of pile-supported ports when subjected to storm surge and waves. The examined structural damage is the uplift of the deck, and the risk assessment is conducted through the development of fragility curves for a typical deck-pile connection, for which fragility curves are developed for different wave models. Uncertainties are also considered in parameters affecting the demand and capacity of the examined deck-pile connection and are propagated through the Monte Carlo simulation using the Latin Hypercube Sampling. The results indicate changes to the uplift probability as a result of the selected wave model. Thus, wave model selection can alter the uplift failure probability. In addition, the study proposes parameterized fragility models to enable the uplift risk assessment across a region. The presented results aim to throw light on the proper model selection to produce more realistic risk assessment estimates towards the resilience of coastal infrastructure. / Thesis / Master of Applied Science (MASc)

This study reports on a new formulation of the spectral dissipation source term Sds for wind-wave modelling applications. This new form of Sds features a nonlinear dependence on the local wave spectrum, expressed in terms of the azimuthally integrated saturation parameter B(k)=k^4 F(k). The basic form of this saturation-dependent Sds is based on a new framework for the onset of deep-water wave breaking due to the nonlinear modulation of wave groups. The new form of Sds is succesfully validated through numerical experiments that include exact nonlinear computations of fetch-limited wind-wave evolution and hindcasts of two-dimensional wave fields made with an operational wind-wave model. The newly-proposed form of Sds generates integral spectral parameters that agree more closely with observations when compared to other dissipation source terms used in state-of-the-art wind-wave models. It also provides more flexibility in controlling properties of the wave spectrum within the high wavenumber range. Tests using a variety of wind speeds, three commonly-used wind input source functions and two alternative full-development evolution limits further demonstrate the robustness and flexibility of the new saturation-dependent dissipation source term. Finally, improved wave hindcasts obtained with an implementation of the new form of Sds in a version of the WAM model demonstrate its potential usefulness in operational wind-wave forecasting applications.

Le secteur de l’énergie houlomotrice s’appuie fortement sur la modélisation mathématique et la simulation d’expériences physiques mettant en jeu les interactions entre les ondes et les corps. Dans ce travail, nous avons développé un modèle d’interaction de fidélité moyenne vague-corps pour la simulation de structures tronquées flottantes fonctionnant en mouvement vertical. Ce travail concerne l’ingénierie de l’énergie marine, pour des applications telles que les convertisseurs d’énergie de vague (WEC) à absorption ponctuelle, même si ses applications peuvent aussi être utilisées en ingénierie maritime et navale. Les motivations de ce travail reposent sur les méthodes standard actuelles pour décrire l’interaction corps-vague. Cellesci sont basées sur des modèles résolvant le flux de potentiel linéaire (LPF), du fait de leur grande efficacité. Cependant, les modèles LPF sont basés sur l’hypothèse de faible amplitude et ne peuvent pas répresenter les effets hydrodynamiques non linéaires, importants pour le WEC opérant dans la région de résonance ou dans les régions proches du rivage. En effet, il a été démontré que les modèles LFP prédisent de manière excessive la production de puissance, sauf si des coefficients de traînée sont calibrés. Plus récemment, des simulations Reynolds Averaged Navier-Stokes (RANS) ont été utilisées pour les WEC. RANS est un modèle complet et précis, mais très coûteux en calcul. Il n’est ni adapté à l’optimisation d’appareils uniques ni aux parcs énergétiques. Nous avons donc proposé un modèle de fidélité moyenne basé sur des équations de type Boussinesq, afin d’améliorer le compromis entre précision et efficacité. Les équations de type Boussinesq sont des modèles d’ondes intégrées en profondeur et ont été un outil d’ingénierie standard pour la simulation numérique de la propagation d’ondes non linéaires dans les eaux peu profondes et les zones côtières. Grâce à l’élimination de la dimension verticale, le modèle résultant est très efficace et évite la description temporelle de la limite entre la surface libre et l’air. Jiang (2001) a proposé un modèle de Boussinesq unifié, décomposant le problème en deux domaines : surface libre et corps. Dans cette méthode, le domaine du corps est également modélisé par une approche intégrée en profondeur - d’où le terme unifié. Récemment, Lannes (2016) avait analysé de manière rigoureuse une configuration similaire dans une équation non linéaire en eaux peu profondes, en déduisant une solution exacte et semi-analitique pour des corps en mouvement. Suivant la même approche, Godlewski et al. (2018) a élaboré un modèle de flux d’eau peu profonde encombrée. [...] Dans cette thèse, nous développons les résultats présentés par Eskilsson et al. (2016) et Bosi et al. (2019). Le modèle est étendu à deux dimensions horizontales. Le modèle 1D est vérifié à l’aide de solutions fabriquées et validé par rapport aux résultats publiés sur l’interaction vague-corps en 1D pour les pontons fixes et corps en mouvement de soulèvement forcé et libre. Les résultats des preuves de concept de la simulation de plusieurs corps sont présentés. Nous validons et vérifions le modèle 2D en suivant des étapes similaires. Enfin, nous mettons en oeuvre la technique de verrouillage, une méthode de contrôle de mouvement du corps pour améliorer la réponse au mouvement des vagues. Il est démontré que le modèle possède une excellente précision, qu’il est pertinent pour les applications d’ondes en interaction avec des dispositifs à énergie houlomotrice et qu’il peut être étendu pour simuler des cas plus complexes. / The wave energy sector relies heavily on mathematical modelling and simulation of the interactions between waves and floating bodies. In this work, we have developed a medium-fidelity wave-body interaction model for the simulation of truncated surface piercing structures operating in heave motion, such as point absorbers wave energy converters (WECs). The motivation of the work lies in the present approach to wave-body interaction. The standard approach is to use models based on linear potential flow (LPF). LPF models are based on the small amplitude/ small motion assumption and, while highly computational efficient, cannot account for nonlinear hydrodynamic effects (except for Morison-type drag). Nonlinear effects are particularly important for WEC operating in resonance, or in nearshore regions where wave transformations are expected. More recently, Reynolds Averaged Navier-Stokes (RANS) simulations have been employed for modelling WECs. RANS is a complete and accurate model but computationally very costly. At present RANS models are therefore unsuited for the optimization of single devices, not to mention energy farms. Thus, we propose a numerical model based built on Boussinesq-type equations to include wave-wave interaction as well as finite body motion in a computationally efficient formulation. Boussinesq-type equations are depth-integrated wave models and are standard engineering tool for numerical simulation of propagation of nonlinear wave in shallow water and coastal areas. Thanks to the elimination of the vertical dimension and the avoidance of a time-dependent computational the resulting model is very computational efficient. Jiang (Jiang, 2001) proposed a unified Boussinesq model, decomposing the problem into free surface and body domains. Notably, in Jiang’s methodology also the body domain is modeled by a depth-integrated approach –hence the term unified. As all models based on Boussinesq-type equations, the model is limited to shallow and intermediate depth regimes. We consider the Madsen and Sørensen model, an enhanced Boussinesq model, for the propagation of waves. We employ a spectral/hp finite element method (SEM) to discretize the governing equations. The continuous SEM is used inside each domain and flux-based coupling conditions are derived from the discontinuous Galerkin method. The use of SEM give support for the use of adaptive meshes for geometric flexibility and high-order accurate approximations makes the scheme computationally efficient. In this thesis, we present 1D results for the propagation and interaction of waves with floating structures. The 1D model is verified using manufactured solutions. The model is then validated against published results for wave-body interaction. The hydrostatic cases (forced motion and decay test) are compared to analytical and semi-analytical solutions (Lannes, 2017), while the non-hydrostatic tests (fixed pontoon and freely heaving bodies) are compared to RANS reference solutions. The model is easily extended to handle multiple bodies and a proof-of-concept result is presented. Finally, we implement the latching technique, a method to control the movement of the body such that the response to the wave movement is improved. The model is extended to two horizontal dimensions and verified and validated against manufactured solutions and RANS simulations. The model is found to have a good accuracy both in one and two dimensions and is relevant for applications of waves interacting with wave energy devices. The model can be extended to simulate more complex cases such as WEC farms/arrays or include power generation systems to the device.

The subject of the thesis is the investigation of asymptotic properties of solutions of the Cauchy problem for structurally damped sigma-evolution operators with time dependent, monotonous, dissipation term. An appropriate energy for solutions of the sigma-evolution equations is defined and some estimates for energies of higher order are proved. In the scale invariant case the optimality of these estimates is shown. Further, the influence of properties of the time dependent dissipation on L^p-L^q estimates for the energy with p and q bigger or equal to 2 and from the conjugate line is clarified. Also smoothing properties of the operators under consideration are investigated. The connection between the regularity of the data and the regularity of the solution in terms of L^2 based Gevrey spaces is considered. Finally, L^1-L^1-estimates in the special case delta = sigma/2 and decreasing dissipative coefficient. / Thema der vorliegenden Dissertation ist die Untersuchung asymptotischer Eigenschaften von Lösungen des Cauchy Problems für strukturell gedämpfte sigma-Evolutions-Operatoren mit zeitabhängigem, monotonen Dissipationskoeffizienten. Es wird eine geeignete Energie definiert und für diese Abschätzungen, auf für entsprechende Energien höherer Ordnung gezeigt. Darüber hinaus wird der Einfluss des Dissipationskoeffizienten auf L^p-L^q Abschätzungen auf und entfernt von der konjugierten Linie untersucht. Im skaleninvarianten Fall wird die Schärfe der Abschätzungen bewiesen. Weiterhin wird der Zusammenhang zwischen der Regularität der Daten und der der Lösung in Termen von L^2-basierten Gevrey-Räumen untersucht. Schließlich werden L^1-L^1-Abschätzungen für den Spezialfall delta = sigma/2 und monoton fallenden Dissipationskoeffizienten gezeigt.

Hurricane hazards result from the combined processes of wind, waves, storm surge, and overwash (Lennon et al., 1996). Predicting the severity of these hazards requires immense effort to quantify the processes and then predict how different coastal regions respond to them. A somewhat simpler, but no less daunting task is to begin to predict the hazards due to potential erosion of barrier islands. A four-part scale has been developed by Sallenger (2000) to provide a framework for understanding how barrier islands might respond during extreme storm events. These four regimes describe how beach and dune elevations interact with surge and wave runup. This study will produce estimates of potential hazards through combining lidar surveys of dune elevation with modeled elevations of storm water levels. Direct measurements of maximum wave heights during hurricanes are rare. We evaluated three simple equations proposed by Kjerfve (1986), Young (1988), and Hsu (1998) to forecast the maximum wave height (Hmax) generated by three 1999 hurricanes. Model results were compared to wave data recorded by the National Oceanic and Atmospheric Administration (NOAA) wave rider buoys. The radius of maximum winds, wind speed, forward velocity, distance from buoy to the storm's eye-wall (r), and buoy's position relative to the quadrant of the storm (Q) were found to have significant and direct roles in evaluating recorded hurricane induced wave heights (H) and thus, were individually examined for each comparison. The implications of the r and Q on H were assessed when determining the overall effectiveness of the modelers' equations. Linear regression analyses tested the accuracy of each modeled prediction of the Hmax, comparing it to the observed wave heights. Three statistical criteria were used to quantify model performance. Hsu's model was the most reliable and useful forecasting technique. Despite the predictive skill of Hsu's model, direct observations of the maximum wave conditions, when available and appropriate, are preferred as inputs for SWAN, a 3rd generation shoaling wave model. Outputs from SWAN are used to calculate the empirical relationships for wave runup. For our test case, pre and post-storm topographies were surveyed as part of a joint USGS-NASA program using lidar technology. These data sets were used to calculate changes in the elevation and location of the dune crest (Dhigh) and dune base (Dlow) for the North Carolina Outer Banks. We hindcast potential coastal hazards (erosional hot spots) using the pre-storm morphology and modeled wave runup and compare those estimates to the measured results from the post-storm survey. Links among the existing topography and spatial variations in wave runup were found to be 95% correlated for the north-south and east-west facing barrier islands. Application of Sallenger's (2000) four-part Storm Impact Scale to the pre-storm Dhigh elevation survey and wave runup extremes (Rhigh and Rlow) were found to accurately predict zones of overwash and showed potential to forecast the inundation regime.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20897号 / 理博第4349号 / 新制||理||1624(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 川畑 貴裕, 教授 永江 知文, 教授 鶴 剛 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Structural Health Monitoring (SHM) systems for future structures and vehicles would involve a process of damage identification and prediction of certain quantities of interest that concerns the function and safety. This process provides SHM systems the ability to not only save cost but also enhance the service life, safety and reliability of the structures and vehicles. Integrated SHM system (ISHM) is an advancement of SHM system that has additional capability of predicting the component life/failure. ISHM system development involves detailed understanding of diagnostic waves, hardware components, signal processing paradigms and intelligent use of algorithms. Diagnostic waves like the guided waves are the elastic waves that propagate in a direction defined by the material boundaries. These waves have the capability of traveling large distance probing the entire thickness in plates/shells. Thus, they are widely used by SHM systems in monitoring the plate structures. Piezoelectric transducers are often employed in the interrogation using guided waves. Most SHM systems employing guided waves are designed for specific structures. Current paradigms of SHM systems are unable to enable the transition from simple or ideal structures to realistic and complicated structures. This is due to the challenges at the fundamental level involving transducer, wave propagation and phenomena of guided wave scattering with damages to evaluate the possible solutions through mathematical modeling and signal analysis capability required by ISHM systems. This thesis aims to develop understanding of these problems at a fundamental level. Complex system level understanding is still needed which is left out as open problem. A primary requirement in designing SHM system is the proper understanding of wave characteristics such as number of modes, wavelength and dispersiveness. Although three-dimensional elasticity solution and simplified theories are available to understand them, their applicability in SHM problem requires a much more detailed look. Effort toward this direction has led to the development of simpler models. However, mathematical models are not available for understanding the wave characteristics in complex structures involving stiffeners and adhesive joints. This problem is addressed in this thesis. There is a fair amount of understanding developed regarding transducer characteristics. This is accomplished by analytical and finite element models of transducers in the past. However, simplified transducer model that are computationally fast to suit SHM system requirements needs to be developed. The development of such model is presented in this thesis. Apart from modeling the transducers and wave scattering due to damage, signal correlation and calibration are needed for practical implementation in SHM. Characterization studies reported in published literature are limited to quasi-static and low frequencies applications. However, SHM of aerospace structures employ guided waves typically in the frequency range of 100-500 kHz. Methods to characterize the transducers at this frequency range needs to be developed, which is addressed in this thesis. Another major requirement of SHM system is the design and development of sensor-actuator network and appropriate algorithm. Techniques developed earlier involving transducer arrays in this regard have limitation due to complexity of geometry and signal interpretation that needs to be addressed. The network with suitable algorithm should ideally monitor large area including the critical areas of failure with minimum number of transducers. ISHM systems further require some capability to estimate the useful life of the damaged structure in order to take suitable decisions. Efficient techniques to achieve these are not developed. Overall, there is a need to improve highly interdisciplinary areas involving mathematical modeling, transducer design, fabrication and characterization, damage detection and monitoring strategies. In this thesis, various novel techniques to combine mathematical model with experimental signals to enhance the damage detection capability are presented. In this thesis, developments in the three main aspects of SHM systems are focused upon. They are (1) development of mathematical models of sensors/actuators, wave propagation and scattering due to damage (2) characterization and calibration of transducers and (3) development of technique to monitor wide variety of damages within the scope of ultrasonic guided wave based SHM. The thesis comprises of ten chapters. First chapter is devoted to the background and motivation for the problem addressed in this thesis. In second chapter, brief overview of available mathematical models and conventional damage monitoring strategy is presented. The significant contributions reported in the subsequent chapters in this thesis are outlined below In chapter 3, a reduced-order model of guided wave propagation in thick structures with reduced-order approximation of higher-order elasto-dynamic field is formulated. The surface normal and shear tractions of the thick structure are satisfied in a closed form. The time-frequency Fourier spectral finite element is developed and is validated using detailed and computationally intensive finite element simulations. Natural frequencies obtained from the developed spectral finite element and the detailed finite element simulations are compared. Transient response due to broad frequency band and narrow frequency band excitations given in the form of surface tractions are validated by comparing with the detailed finite element simulations. Using the developed spectral finite element, wave scattering from a free edge and a notch are simulated and validated by comparing with the detailed finite element simulations. In chapter 4, two-dimensional plane wave and flexural wave scattering models for more complicated features such as stiffener with delamination and stiffener with bolt failures in a stiffened panel are derived using ultrasonic ray tracing based approach combined with wave-field representation. Dispersion relations are reformulated for the base plate where it is bolted with the stiffener. Surface conditions due to contact stiffness and contact damping are modeled by introducing springs and dampers. Scattering coefficients for the bonded and bolted stiffeners are derived. The scattering coefficients are evaluated for various different frequencies. Results are compared for different stiffener parameters. In chapter 5, a simplified analytical model of a piezoelectric actuator with uniform electrodes is modeled. The problem is to determine the launched guided wave characteristics in the structure. The analytical model is derived considering two-dimensional elasticity based approach and Airy’s stress function. The actuator model is used to specify the displacement boundary conditions in the detailed finite element model. The radiated wave patterns in a plate due to actuation from transducers of different shapes are obtained and validated with experiments. Phased array actuators are modeled in the detailed finite element model using the displacements estimated from the actuator model. The radiated wave pattern from the detailed finite element simulations are validated with experiments. Chapter 6 is devoted to the design and characterization of transducers for ultrasonic guided wave applications. The characterization techniques involve the estimation of voltage response for the induced strain by the guided wave at various different frequencies. First, a novel removable bonding technique and a calibration technique are demonstrated and related advantages are discussed. Performance of the piezoelectric thin film under quasi-static, dynamic and transient impact loadings are analyzed first. Next, a guided wave technique is developed to characterize piezoelectric thin film sensors and actuators at ultrasonic frequencies. The transducers with inter digital electrodes are characterized for frequency tuning and directional sensitivity. This characterization study enables in the selection of optimal frequency bands for interrogation. Further, the characterization of transducers with thermal degradation is presented. In chapter 7, a novel guided wave technique to calibrate the thin film sensors for ultrasonic applications is presented. Calibration procedure involves the estimation of the piezoelectric coefficient at ultrasonic range of frequencies. Calibration is done by the measurement of voltage generated across thin films when guided waves are induced on them. With the proposed technique, piezoelectric coefficient can be estimated accurately at any frequency of the propagating wave. Similarly, the measurement of piezoelectric coefficient of thin films with inter digital electrodes is presented. The estimation of piezoelectric coefficient at various different directions using laser Doppler vibrometer is presented. Lastly, the degradation of piezoelectric coefficient is studied for increasing thermal fatigue. In chapter 8, toward SHM methodology development, a guided wave based technique to detect and monitor cracks in a structure is presented. To establish the methodology, a detailed study is carried out on the effect of crack and specimen size on the guided wave propagation characteristics. Using the wave characteristics, an analytical way of modeling Lamb wave propagation in the specimen with plastic zone is proposed. The feasibility to determine plastic zone and fatigue crack propagation with integrated piezoelectric transducers is demonstrated experimentally and the results are verified analytically. A method is further established to detect damage at initial stage and crack-tip plastic zone size along with crack length for a given stress amplitude or vice-versa. An approach to estimate fatigue life from the transducer signals is also proposed. In chapter 9, a compact circular array of sensor-actuator network and an algorithm is presented to monitor large plate structures. A method based on the wavelet transforms of transducer signals is established to localize and estimate the severity of damages. Experiments are conducted to demonstrate the capability of the circular array based method in the localization and quantification of various types of damages like debonding of stiffeners, failure of bolted joints, corrosion and hole-enlargement. A damage index is then computed from wavelet time-frequency map that indicates the severity of damage. Chapter 10 ends with the concluding remarks on the work done with simultaneous discussion on the future scope. The work reported in this thesis is interdisciplinary in nature and it aims to combine the modeling and simulation techniques with realistic data in SHM to impart higher confidence levels in the prediction of damages and its prognosis. The work also aims in incorporating various mathematical models of wave propagation and ray tracing based algorithm to optimize the detection scheme employed in SHM. The future direction based on this study could be aimed at developing intelligent SHM systems with high confidence levels so that statistical machine learning would be possible to deal with complex real-world SHM problems.

The subject of the thesis is the investigation of asymptotic properties of solutions of the Cauchy problem for structurally damped sigma-evolution operators with time dependent, monotonous, dissipation term. An appropriate energy for solutions of the sigma-evolution equations is defined and some estimates for energies of higher order are proved. In the scale invariant case the optimality of these estimates is shown. Further, the influence of properties of the time dependent dissipation on L^p-L^q estimates for the energy with p and q bigger or equal to 2 and from the conjugate line is clarified. Also smoothing properties of the operators under consideration are investigated. The connection between the regularity of the data and the regularity of the solution in terms of L^2 based Gevrey spaces is considered. Finally, L^1-L^1-estimates in the special case delta = sigma/2 and decreasing dissipative coefficient. / Thema der vorliegenden Dissertation ist die Untersuchung asymptotischer Eigenschaften von Lösungen des Cauchy Problems für strukturell gedämpfte sigma-Evolutions-Operatoren mit zeitabhängigem, monotonen Dissipationskoeffizienten. Es wird eine geeignete Energie definiert und für diese Abschätzungen, auf für entsprechende Energien höherer Ordnung gezeigt. Darüber hinaus wird der Einfluss des Dissipationskoeffizienten auf L^p-L^q Abschätzungen auf und entfernt von der konjugierten Linie untersucht. Im skaleninvarianten Fall wird die Schärfe der Abschätzungen bewiesen. Weiterhin wird der Zusammenhang zwischen der Regularität der Daten und der der Lösung in Termen von L^2-basierten Gevrey-Räumen untersucht. Schließlich werden L^1-L^1-Abschätzungen für den Spezialfall delta = sigma/2 und monoton fallenden Dissipationskoeffizienten gezeigt.