Identification of an unknown spatial load distribution in a vibrating beam or plate from the final state

The theoretical and numerical determination of a space-dependent load distribution in a simply supported non-homogeneous Euler-Bernoulli beam and Kirchhoff-Love plate is investigated. The uniqueness of a solution to this inverse source problem is proved, whilst counter examples are constructed to discuss the conditions under which uniqueness holds. A convergent and stable iterative algorithm is proposed for the recovery of the unknown load source and a stopping criterion is also given. Several one-dimensional numerical experiments are considered to investigate the properties of the proposed iterative procedure

Thermoelastic and photoelastic full-field stress measurement

Photoelasticity is an optical technique that measures the difference of the principal stresses plus the principal stress direction. A complementary technique is thermoelasticity which measures the sum of the principal stresses. Combining these two full-field, non-contact nondestructive evaluation techniques allows the individual stress components to be measured. One of the main difficulties in merging these two measurement systems is in identifying an appropriate surface coating. Thermoelasticity demands a highly emissive surface, while photoelasticity requires a thick, stress-birefringent, transparent coating with a retro-reflective backing. Two coatings have been identified that can be used for combined thermoelastic and photoelastic stress measurements: PMMA and polycarbonate.;An anisotropic electromagnetic boundary value model was developed to understand more fully the mechanisms through which photoelastic stress patterns are produced. This model produced intensity contour maps which matched the fringe patterns observed in the laboratory, and allowed the effect of measurement errors on the calculated stress tensor to be quantified. One significant source of error was the retro-reflective backing, which depolarized the light and degraded the resulting photoelastic fringes. A quantitative analysis of the degraded fringes, to be used as a rating scheme for reflective backing materials, showed that the isoclinic lines shift position as a result of the backing roughness and oblique incidence. This is a concern when calculating the stress components through the combination of photoelasticity and thermoelasticity because the data maps are integrated at the pixel level. Small shifts in the photoelastic fringes result in incorrect information being assigned to some pixels and hence lead to uncertainties in the stress tensor components. Progress in the understanding of the depolarization at the reflective backing allows the specification of new materials that will minimize this effect, as well as the development of robust computer algorithms to correct for any remaining depolarization

Thermoelastic and photoelastic full-field stress measurement

Photoelasticity is an optical technique that measures the difference of the principal stresses plus the principal stress direction. A complementary technique is thermoelasticity which measures the sum of the principal stresses. Combining these two full-field, non-contact nondestructive evaluation techniques allows the individual stress components to be measured. One of the main difficulties in merging these two measurement systems is in identifying an appropriate surface coating. Thermoelasticity demands a highly emissive surface, while photoelasticity requires a thick, stress-birefringent, transparent coating with a retro-reflective backing. Two coatings have been identified that can be used for combined thermoelastic and photoelastic stress measurements: PMMA and polycarbonate.;An anisotropic electromagnetic boundary value model was developed to understand more fully the mechanisms through which photoelastic stress patterns are produced. This model produced intensity contour maps which matched the fringe patterns observed in the laboratory, and allowed the effect of measurement errors on the calculated stress tensor to be quantified. One significant source of error was the retro-reflective backing, which depolarized the light and degraded the resulting photoelastic fringes. A quantitative analysis of the degraded fringes, to be used as a rating scheme for reflective backing materials, showed that the isoclinic lines shift position as a result of the backing roughness and oblique incidence. This is a concern when calculating the stress components through the combination of photoelasticity and thermoelasticity because the data maps are integrated at the pixel level. Small shifts in the photoelastic fringes result in incorrect information being assigned to some pixels and hence lead to uncertainties in the stress tensor components. Progress in the understanding of the depolarization at the reflective backing allows the specification of new materials that will minimize this effect, as well as the development of robust computer algorithms to correct for any remaining depolarization

Proper orthogonal decomposition, dynamic mode decomposition, wavelet and cross wavelet analysis of a sloshing flow

Internal hydrodynamics and its coupling with structural dynamics are non-negligible processes in the design phase of aerospace systems. An improved understanding of the nature of this coupling would allow for greater flexibility in modeling and design of such systems, and could lead eventually to the development of suitable active and/or passive control strategies for enhanced performances. In this manuscript we apply a number of data analysis techniques: proper orthogonal decomposition, dynamic mode decomposition and wavelet transform and their combination to time-resolved images of a liquid sloshing within an enclosure. We use these techniques to identify fluid-dynamic modes in space and time and to verify their coupling with the structural dynamics of vibrating structures. In particular we consider the transient case of a water tank mounted on a free oscillating cantilever. As the acceleration amplitude decays, we observe and quantify the transition from incoherent flow to standing waves. Our results show that the content of the images is very informative and can be used for quantitative analysis. As the main outcome, the hydrodynamic modes are identified using POD and DMD, and related to known features of sloshing flow, such as the frequency of the first symmetric free surface mode. Additionally we perform a comparison of wavelet transforms of POD time coefficients and measured acceleration signals at the tank base. Viewing the latter as the input and the former as the output of the fluid-dynamic system, we are able to correlate the enhanced damping of the cantilever oscillation to the different regimes of the hydrodynamic field

Acoustic interference fields in the ocean

Two areas of underwater acoustics are investigated: ocean-bottom scattering and acoustic fields in geometrically dispersive sound channels. The purpose is to describe and provide an understanding of the physical mechanisms in these two areas by comparing analyzed results from ocean experiments with theoretical computations. Experiments using directive 19.5-kHz transducers illustrate temporal and spacial behavior of signals scattered from the ocean bottom. The signals fluctuate, as a function of acoustic geometry, in linear relation to source and receiver motion and to signal frequency. Spacial structure of the acoustic field depends on frequency and acoustic geometry and is independent of motion and bottom roughness. Data supporting these observations are included as well as data showing the effects of bottom type on the scattered returns, that is, the existence of subbottom returns in some data. Volume-scattering-strength profiles are also provided from data obtained in these experiments. Continuous-wave (CW) and impulsive sources covering frequencies 5 to 260 Hz were towed and deployed respectively over ranges up to 3000 km, with reception on fixed hydrophones. Analyses of measured propagation losses of these low-frequency acoustic signals in the dispersive channel provide insights into the nature of the propagation and the acoustic channel. Both the CW signals and the arrivals of the impulsive signals are analyzed in terms of transmission loss, convergence-zone structure, source-motion effects, interference structure, and channel characteristics. The systematic variation (internal tides) of the medium and its influence on the interference field are discussed. The state of modeling, both simple and complicated, is reviewed and compared with results of the ocean experiments. Relationships are provided between this work and the broader field of underwater acoustics. Suggested areas for future research are made

A study of the mechanics of microcantilever sensors

Microcantilever sensors are being studied as a new platform for chemical vapor detection. It has been demonstrated by many groups that they have the potential to detect a wide range of chemicals with high sensitivity. Since these sensors do not offer any intrinsic chemical selectivity, immobilized chemical interfaces coupled with pattern recognition algorithms are often employed. Selectivity based on these chemical coatings often fails due to the lack of orthogonality in the chemical interactions. However, the use of adsorption-induced signals based on physical properties can offer additional complementary information. To successfully employ these versatile sensors, a comprehensive investigation of the mechanics of microcantilevers is necessary to understand their responses. Such an investigation is presented in this work. Both dynamic and static microcantilever theory is addressed as well as nonlinear dynamics resulting from large amplitude oscillations. Experimental data is presented and compared to modeled data for verification. Finally, an application of microcantilever sensors in photothermal deflection spectroscopy (PDS) is given. The detection of explosive compounds with PDS is demonstrated

Control system implementation on an AFM prototype

Tese de Mestrado Integrado, Engenharia Física, 2022, Universidade de Lisboa, Faculdade de CiênciasThis work deals with the implementation of a fine and coarse tip-sample distance control as well as with the tuning of several other features that will make one AFM prototype more user friendly. The main goal was to design and integrate a PI (Proportional-Integral) Analog Controller with digitally controllable gains. The development of the controller started by identifying and characterizing the system, with emphasis on the Z-axis Scanner’s response, which in turn allowed to build models for all the different components that make up the AFM. The PI Controller’s gains were arranged to be independently tuned via a digital potentiometer in conjunction with an analog multiplexer. The digital potentiometer provides a fine gain adjustment while the analog multiplexer increments the gains by an order of magnitude. These devices receive instructions from a microcontroller. In parallel, several other important enhancements were carried out, which include an implementation of an Auto-Approach functionality that automatically approaches the probe and sample without crashing onto each other. In order to achieve this, it was conducted an experimental study of the instrument’s motorized coarse motion structure. All the new features developed here were integrated in the existing prototype via the Arduino platform. To interface the signals outputted by the AFM circuitry and the microcontroller, as well as providing robust tolerance against faulty use, additional circuitry was included. This allows the reading of important signals within the instrument’s context, such as the deflection signal, amplitude signal and controller output. By taking advantage of the microcontroller’s features, it was designed a voltage source that serves as an adjustable setpoint via the PWM outputs from the Arduino. Finally, it was design and developed a GUI providing the user direct control of the tasks mentioned above and also displaying some quantitative and qualitative data, acquired by the microcontroller, about the state of the AFM

Non-linear model fitting for the measurement of thin films and surface topography

Inspection of optical components is essential to assure the quality and performance of optical systems. Evaluation of optical components includes metrology measurements of surface topography. It also requires optical measurements including refractive index, thin film thickness, reflectivity and transmission. The dispersion characteristics of optical constants including refractive index are also required. Hence, various instruments are used to make these measurements in research laboratories and for quality assurance. Clearly, it would be a significant advantage and cost saving if a technique was developed that could combine surface metrology with optical measurements. {Coherence Scanning Interferometry} (CSI) (also referred to as {Scanning White Light Interferometry} (SWLI)) has been used widely to measure surface topography with sub-nanometre vertical resolution. One of the benefits of the CSI is that the technique is non-contacting and hence non-destructive. Thus the test surfaces are not affected by the measurement using a CSI instrument whereas damage to the surfaces can occur when using traditional contact methods such as stylus profilometry. However use of CSI is geometrically limited to small areas ($\lesssim 10 \times 10$ mm) with gentle slopes (\lesssim \ang{40}) because of the numerical aperture of objective lens whereas stylus profilometry works well with larger areas and higher slopes due to the range of motion of the gauge and the traverse unit. Since the CSI technique is optical and involves light reflection and interference it is possible to extend the technique for the measurement of the thickness of transparent films, the roughness of surfaces buried beneath thin films or interfacial surfaces. It may also be used to determine spectral complex refractive index. This thesis provides an analytical framework of new methods to obtain complex refractive index in a visible light domain and interfacial surface roughness (ISR). It also provides experimental verification of these new capabilities using actual thin film model systems. The original Helical Complex Field (HCF) function theory is presented followed by its existing extensions that enable determination of complex refractive index and interfacial surface roughness. Further theoretical extensions of the HCF theory are also provided: A novel theory to determine the refractive index of a (semi-)transparent film is developed to address the constraint of the current HCF theory that restricted its use to opaque materials; Another novel theory is provided to measure ISR with noise compensation, which avoids erroneous surface roughness caused by the numerical optimisation affected by the existence of noise. The effectiveness of the ISR measurement with noise compensation has been verified using a number of computer simulations. Stylus profilometry is a well established method to provide a profile and has been used extensively as a 'reference' for other techniques. It normally provides a profile on which the roughness and the waviness are computed. Extension of the stylus profilometry technique to areal measurement of asymmetrical surfaces, namely raster scan measurement, requires a system to include error compensation between each traverse. The system errors and the random errors need to be separately understood particular when the measurement of a surface with nanometre-order accuracy is required. In this thesis a mathematical model to locate a stylus tip considering five mechanical errors occurring in a common raster scan profilometer is provided. Based on the model, the simulator which provides an areal measurement of a sphere was developed. The simulator clarified the relationship between the Zernike coefficients obtained from the form residual and the size of the errors in the form of partial derivatives of Zernike coefficients with respect to the errors. This provides theoretical support to the empirical knowledge of the relationship between the coefficients and the errors. Furthermore, a method to determine the size of errors directly from Zernike coefficients is proposed supported by simulations. Some of the error parameters were accurately determined avoiding iterative computation with this method whereas the errors are currently being determined by iterative computation