Numerical methods for the dispersion analysis of Guided Waves

The use of guided ultrasonic waves (GUW) has increased considerably in the fields of non-destructive (NDE) testing and structural health monitoring (SHM) due to their ability to perform long range inspections, to probe hidden areas as well as to provide a complete monitoring of the entire waveguide. Guided waves can be fully exploited only once their dispersive properties are known for the given waveguide. In this context, well stated analytical and numerical methods are represented by the Matrix family methods and the Semi Analytical Finite Element (SAFE) methods. However, while the former are limited to simple geometries of finite or infinite extent, the latter can model arbitrary cross-section waveguides of finite domain only. This thesis is aimed at developing three different numerical methods for modelling wave propagation in complex translational invariant systems. First, a classical SAFE formulation for viscoelastic waveguides is extended to account for a three dimensional translational invariant static prestress state. The effect of prestress, residual stress and applied loads on the dispersion properties of the guided waves is shown. Next, a two-and-a-half Boundary Element Method (2.5D BEM) for the dispersion analysis of damped guided waves in waveguides and cavities of arbitrary cross-section is proposed. The attenuation dispersive spectrum due to material damping and geometrical spreading of cavities with arbitrary shape is shown for the first time. Finally, a coupled SAFE-2.5D BEM framework is developed to study the dispersion characteristics of waves in viscoelastic waveguides of arbitrary geometry embedded in infinite solid or liquid media. Dispersion of leaky and non-leaky guided waves in terms of speed and attenuation, as well as the radiated wavefields, can be computed. The results obtained in this thesis can be helpful for the design of both actuation and sensing systems in practical application, as well as to tune experimental setup.

Non-Linear Analysis and Design of Synchronous Bearingless Multiphase Permanent Magnet Machines and Drives

A two-dimensional model to analyze the distribution of magnetic fields in the airgap of a PM electrical machines is studied. A numerical algorithm for non-linear magnetic analysis of multiphase surface-mounted PM machines with semi-closed slots is developed, based on the equivalent magnetic circuit method. By using a modular structure geometry, whose the basic element can be duplicated, it allows to design whatever typology of windings distribution. In comparison to a FEA, permits a reduction in computing time and to directly changing the values of the parameters in a user interface, without re-designing the model. Output torque and radial forces acting on the moving part of the machine can be calculated. In addition, an analytical model for radial forces calculation in multiphase bearingless Surface-Mounted Permanent Magnet Synchronous Motors (SPMSM) is presented. It allows to predict amplitude and direction of the force, depending on the values of torque current, of levitation current and of rotor position. It is based on the space vectors method, letting the analysis of the machine also during transients. The calculations are conducted by developing the analytical functions in Fourier series, taking all the possible interactions between stator and rotor mmf harmonic components into account and allowing to analyze the effects of electrical and geometrical quantities of the machine, being parametrized. The model is implemented in the design of a control system for bearingless machines, as an accurate electromagnetic model integrated in a three-dimensional mechanical model, where one end of the motor shaft is constrained to simulate the presence of a mechanical bearing, while the other is free, only supported by the radial forces developed in the interactions between magnetic fields, to realize a bearingless system with three degrees of freedom. The complete model represents the design of the experimental system to be realized in the laboratory.

Techniques and Methods for a multi-scale analysis of neuromuscular fatigue

This thesis proposes an integrated holistic approach to the study of neuromuscular fatigue in order to encompass all the causes and all the consequences underlying the phenomenon. Starting from the metabolic processes occurring at the cellular level, the reader is guided toward the physiological changes at the motorneuron and motor unit level and from this to the more general biomechanical alterations. In Chapter 1 a list of the various definitions for fatigue spanning several contexts has been reported. In Chapter 2, the electrophysiological changes in terms of motor unit behavior and descending neural drive to the muscle have been studied extensively as well as the biomechanical adaptations induced. In Chapter 3 a study based on the observation of temporal features extracted from sEMG signals has been reported leading to the need of a more robust and reliable indicator during fatiguing tasks. Therefore, in Chapter 4, a novel bi-dimensional parameter is proposed. The study on sEMG-based indicators opened a scenario also on neurophysiological mechanisms underlying fatigue. For this purpose, in Chapter 5, a protocol designed for the analysis of motor unit-related parameters during prolonged fatiguing contractions is presented. In particular, two methodologies have been applied to multichannel sEMG recordings of isometric contractions of the Tibialis Anterior muscle: the state-of-the-art technique for sEMG decomposition and a coherence analysis on MU spike trains. The importance of a multi-scale approach has been finally highlighted in the context of the evaluation of cycling performance, where fatigue is one of the limiting factors. In particular, the last chapter of this thesis can be considered as a paradigm: physiological, metabolic, environmental, psychological and biomechanical factors influence the performance of a cyclist and only when all of these are kept together in a novel integrative way it is possible to derive a clear model and make correct assessments.

Three-dimensional joint kinematics of swimming using body-worn inertial and magnetic sensors

Wearable inertial and magnetic measurements units (IMMU) are an important tool for underwater motion analysis because they are swimmer-centric, they require only simple measurement set-up and they provide the performance results very quickly. In order to estimate 3D joint kinematics during motion, protocols were developed to transpose the IMMU orientation estimation to a biomechanical model. The aim of the thesis was to validate a protocol originally propositioned to estimate the joint angles of the upper limbs during one-degree-of-freedom movements in dry settings and herein modified to perform 3D kinematics analysis of shoulders, elbows and wrists during swimming. Eight high-level swimmers were assessed in the laboratory by means of an IMMU while simulating the front crawl and breaststroke movements. A stereo-photogrammetric system (SPS) was used as reference. The joint angles (in degrees) of the shoulders (flexion-extension, abduction-adduction and internal-external rotation), the elbows (flexion-extension and pronation-supination), and the wrists (flexion-extension and radial-ulnar deviation) were estimated with the two systems and compared by means of root mean square errors (RMSE), relative RMSE, Pearson’s product-moment coefficient correlation (R) and coefficient of multiple correlation (CMC). Subsequently, the athletes were assessed during pool swimming trials through the IMMU. Considering both swim styles and all joint degrees of freedom modeled, the comparison between the IMMU and the SPS showed median values of RMSE lower than 8°, representing 10% of overall joint range of motion, high median values of CMC (0.97) and R (0.96). These findings suggest that the protocol accurately estimated the 3D orientation of the shoulders, elbows and wrists joint during swimming with accuracy adequate for the purposes of research. In conclusion, the proposed method to evaluate the 3D joint kinematics through IMMU was revealed to be a useful tool for both sport and clinical contexts.

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.

Analysis of slip distribution of large earthquakes oriented to tsunamigenesis characterisation

The present thesis focuses on the on-fault slip distribution of large earthquakes in the framework of tsunami hazard assessment and tsunami warning improvement. It is widely known that ruptures on seismic faults are strongly heterogeneous. In the case of tsunamigenic earthquakes, the slip heterogeneity strongly influences the spatial distribution of the largest tsunami effects along the nearest coastlines. Unfortunately, after an earthquake occurs, the so-called finite-fault models (FFM) describing the coseismic on-fault slip pattern becomes available over time scales that are incompatible with early tsunami warning purposes, especially in the near field. Our work aims to characterize the slip heterogeneity in a fast, but still suitable way. Using finite-fault models to build a starting dataset of seismic events, the characteristics of the fault planes are studied with respect to the magnitude. The patterns of the slip distribution on the rupture plane, analysed with a cluster identification algorithm, reveal a preferential single-asperity representation that can be approximated by a two-dimensional Gaussian slip distribution (2D GD). The goodness of the 2D GD model is compared to other distributions used in literature and its ability to represent the slip heterogeneity in the form of the main asperity is proven. The magnitude dependence of the 2D GD parameters is investigated and turns out to be of primary importance from an early warning perspective. The Gaussian model is applied to the 16 September 2015 Illapel, Chile, earthquake and used to compute early tsunami predictions that are satisfactorily compared with the available observations. The fast computation of the 2D GD and its suitability in representing the slip complexity of the seismic source make it a useful tool for the tsunami early warning assessments, especially for what concerns the near field.

Experimental and Numerical Analysis of Gas Flows in Microchannels and Micro Heat Exchanger

Due to increased interest in miniaturization, great attention has been given in the recent decade to the micro heat exchanging systems. Literature survey suggests that there is still a limited understanding of gas flows in micro heat exchanging systems. The aim of the current thesis is to further the understanding of fluid flow and heat transfer phenomenon inside such geometries when a compressible working fluid is utilized. A combined experimental and numerical approach has been utilized in order to overcome the lack of employable sensors for micro dimensional channels. After conducting a detailed comparison between various data reduction methodologies employed in the literature, the best suited methodology for gas microflow experimentalists is proposed. A transitional turbulence model is extensively validated against the experimental results of the microtubes and microchannels under adiabatic wall conditions. Heat transfer analysis of single microtubes showed that when the compressible working fluid is used, Nusselt number results are in partial disagreement with the conventional theory at highly turbulent flow regime for microtubes having a hydraulic diameter less than 250 microns. Experimental and numerical analysis on a prototype double layer microchannel heat exchanger showed that compressibility is detrimental to the thermal performance. It has been found that compressibility effects for micro heat exchangers are significant when the average Mach number at the outlet of the microchannel is greater than 0.1 compared to the adiabatic limit of 0.3. Lastly, to avoid a staggering amount of the computational power needed to simulate the micro heat exchanging systems with hundreds of microchannels, a reduced order model based on the porous medium has been developed that considers the compressibility of the gas inside microchannels. The validation of the proposed model against experimental results of average thermal effectiveness and the pressure loss showed an excellent match between the two.

Analysis of the main phenomena affecting solid rocket motors internal ballistics

In solid rocket motors, the absence of combustion controllability and the large amount of financial resources involved in full-scale firing tests, increase the importance of numerical simulations in order to asses stringent mission thrust requirements and evaluate the influence of thrust chamber phenomena affecting the grain combustion. Among those phenomena, grain local defects (propellant casting inclusions and debondings), combustion heat accumulation involving pressure peaks (Friedman Curl effect), and case-insulating thermal protection material ablation affect thrust prediction in terms of not negligible deviations with respect to the nominal expected trace. Most of the recent models have proposed a simplified treatment to the problem using empirical corrective functions, with the disadvantages of not fully understanding the physical dynamics and thus of not obtaining predictive results for different configurations of solid rocket motors in a boundary conditions-varied scenario. This work is aimed to introduce different mathematical approaches to model, analyze, and predict the abovementioned phenomena, presenting a detailed physical interpretation based on existing SRMs configurations. Internal ballistics predictions are obtained with an in-house simulation software, where the adoption of a dynamic three-dimensional triangular mesh together with advanced computer graphics methods, allows the previous target to be reached. Numerical procedures are explained in detail. Simulation results are carried out and discussed based on experimental data.

Numerical and experimental analysis of 3D printed smart structures and systems

Three dimensional (3D) printers of continuous fiber reinforced composites, such as MarkTwo (MT) by Markforged, can be used to manufacture such structures. To date, research works devoted to the study and application of flexible elements and CMs realized with MT printer are only a few and very recent. A good numerical and/or analytical tool for the mechanical behavior analysis of the new composites is still missing. In addition, there is still a gap in obtaining the material properties used (e.g. elastic modulus) as it is usually unknown and sensitive to printing parameters used (e.g. infill density), making the numerical simulation inaccurate. Consequently, the aim of this thesis is to present several work developed. The first is a preliminary investigation on the tensile and flexural response of Straight Beam Flexures (SBF) realized with MT printer and featuring different interlayer fiber volume-fraction and orientation, as well as different laminate position within the sample. The second is to develop a numerical analysis within the Carrera' s Unified Formulation (CUF) framework, based on component-wise (CW) approach, including a novel preprocessing tool that has been developed to account all regions printed in an easy and time efficient way. Among its benefits, the CUF-CW approach enables building an accurate database for collecting first natural frequencies modes results, then predicting Young' s modulus based on an inverse problem formulation. To validate the tool, the numerical results are compared to the experimental natural frequencies evaluated using a digital image correlation method. Further, we take the CUF-CW model and use static condensation to analyze smart structures which can be decomposed into a large number of similar components. Third, the potentiality of MT in combination with topology optimization and compliant joints design (CJD) is investigated for the realization of automated machinery mechanisms subjected to inertial loads.

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Analysis and design considerations of resonator arrays for inductive power transfer systems

In the frame of inductive power transfer (IPT) systems, arrays of magnetically coupled resonators have received increasing attention as they are cheap and versatile due to their simple structure. They consist of magnetically coupled coils, which resonate with their self-capacitance or lumped capacitive networks. Of great industrial interest are planar resonator arrays used to power a receiver that can be placed at any position above the array. A thorough circuit analysis has been carried out, first starting from traditional two-coil IPT devices. Then, resonator arrays have been introduced, with particular attention to the case of arrays with a receiver. To evaluate the system performance, a circuit model based on original analytical formulas has been developed and experimentally validated. The results of the analysis also led to the definition of a new doubly-fed array configuration with a receiver that can be placed above it at any position. A suitable control strategy aimed at maximising the transmitted power and the efficiency has been also proposed. The study of the array currents has been carried out resorting to the theory of magneto-inductive waves, allowing useful insight to be highlighted. The analysis has been completed with a numerical and experimental study on the magnetic field distribution originating from the array. Furthermore, an application of the resonator array as a position sensor has been investigated. The position of the receiver is estimated through the measurement of the array input impedance, for which an original analytical expression has been also obtained. The application of this sensing technique in an automotive dynamic IPT system has been discussed. The thesis concludes with an evaluation of the possible applications of two-dimensional resonator arrays in IPT systems. These devices can be used to improve system efficiency and transmitted power, as well as for magnetic field shielding.

Analysis of the long-term subsidence in the urban area of Bologna

Land subsidence in urban areas represents a widespread geological hazard and a pressing challenge for modern society. This research focuses on the subsidence process affecting the city of Bologna (Italy). Since the 1960s, Bologna has experienced ground deformation due to aquifers overexploitation that peaked during the 1970s with rates of 10 cm/year. Despite a general reduction in these rates over the subsequent decades, thanks to groundwater regulations policies, recent data underscore a substantial subsidence resurgence. To reconstruct the subsurface stratigraphic architecture of Bologna’s urban area and generate a 3D geological model, a multidisciplinary approach centred on a stratigraphic analysis relying on the lithofacies criterion was adopted. The convergence of the analyses within this framework resulted in partitioning the study area into three geological domains exhibiting unique morphological features and depositional stacking patterns. Subsequently, since long-term data are crucial for a comprehensive understanding of ongoing subsidence, a methodology was developed to generate cumulative ground displacement time series and maps by integrating ground-based and remotely-sensed measurements. While the reconstructed long-term subsidence field consistently aligns with the primary geological variations summarised in the 3D model, the generated cumulative displacement curves systematically match pluriannual trends observed in groundwater level and pumping monitoring data. Lastly, to evaluate the expression of the observed relationships from a geotechnical perspective, a series of one-dimensional subsidence calculations were conducted considering the mechanical properties of the investigated deposits and piezometric data. These analyses provided valuable insight into the overall mechanical behaviour of the existing soils, as well as the post-pumping groundwater level and pore pressure distributions, consistent with field data. The methodological approach employed enables a comprehensive analysis of land subsidence in urban areas, allowing the exploration of individual factors governing the deformation process and their interactions, even within complex stratigraphic and hydrogeological environments such as Bologna’s urban area.