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This thesis study focuses on a particular non-contact vibration measurement technique used in the industry: 1D Laser Doppler Vibrometry. This technique measures
the vibration in the direction of the laser beam, thus captures only a projection of the
phenomenon in 3D. This has been a limiting factor in understanding the real vibration
of an object. The main drive of this study is to understand the capabilities and the
limitations of this technique; and propose a solution to these limitations.
To overcome the limitations arising from measuring tilted or non- at surfaces, a
solution method has been proposed. The proposed method requires a single image input
from the vibration measurement camera and the computer model of the test object.
With this method, measurement coordinate alignment with 3D computer model can
be established and the FRF signals can be corrected to obtain normal-to-surface 3D
mode shape information. Experiments have been done to investigate the validity and
performance of the proposed method.
The results showed that the measurements with 1D Laser Doppler Vibrometry follow
the theoretical expectations under tilt angles. With this information, the measurement
amplitudes could be corrected to derive the normal-to-surface vibrations. However, by
increasing the tilt angle coordinate shifts have been observed regarding the alignment
of measurement points. The shifts have been related to the LDV device con guration.
Unless corrected, the results on non- at surface measurements only give analysis of a
nonlinearly shifted coordinate set, which becomes misleading.

Scanning Laser Doppler Vibrometry, 1D LDV, Modal Analysis, Non-contact Sensing, Non- at Surface Vibration, Vibration Testing, NVH --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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The inverse dynamics problem was developed in order to provide researchers with the state of the art in inverse problems for dynamic and vibrational systems. Contrasted with a forward problem, which solves for the system output in a straightforward manner, an inverse problem searches for the system input through a procedure contaminated with errors and uncertainties. An inverse problem, with a focus on structural dynamics, determines the changes made to the system and estimates the inputs, including forces and moments, to the system, utilizing measurements of structural vibration responses only. With its complex mathematical structure and need for more reliable input estimations, the inverse problem is still a fundamental subject of research among mathematicians and engineering scientists. This book contains 11 articles that touch upon various aspects of inverse dynamic problems.

Technology: general issues --- regenerative shock absorbers --- energy harvesting --- active control of automobile suspension systems --- railroad tracks --- track modulus --- computer simulation --- artificial neural networks --- Fiber-reinforced Foamed Urethane (FFU) --- free vibration --- impact hammer excitation technique --- high-rate dynamics --- structural health monitoring --- time-frequency analysis --- synchrosqueezing transform (SST) --- jerk --- acceleration onset --- higher-order derivatives of acceleration --- jounce --- acceleration-dot --- sports surfacing --- sand surface --- dynamic behaviour --- impact tests --- accelerometry --- greyhound racing --- equine racing --- shake table control --- vibration testing --- system identification --- inverse dynamics --- feedback linearization --- servohydraulics --- inverse problems --- quantum graphs --- delta-prime vertex conditions --- Bayesian inference --- uncertainty quantification --- dynamical systems --- inverse problem --- machine learning --- Gaussian process --- polynomial chaos --- impact force identification --- tower structure --- impact localization --- force history --- inverse algorithm --- rotor dynamic --- bearing --- centrifugal pump --- impeller diameter --- Lagrangian equations --- n/a

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This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

Elasticity --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Mathematics. --- Properties --- Dirichlet function. --- Helmholtz decomposition theorem. --- Helmholtz decomposition. --- HelmholtzЋirchhoff identities. --- Kelvin matrix. --- Kirchhoff migration. --- Lam system. --- MUSIC algorithm. --- Neumann boundary condition. --- anisotropic elasticity. --- asymptotic expansion. --- asymptotic formula. --- asymptotic imaging. --- ball. --- boundary displacement. --- boundary perturbation. --- boundary value problem. --- boundedness. --- cellular structure. --- compressional modulus. --- crack. --- density parameter. --- direct imaging. --- discrepancy function. --- displacement field. --- displacement. --- elastic coefficient. --- elastic equation. --- elastic inclusion. --- elastic moment tensor. --- elastic structure. --- elastic wave equation. --- elastic wave propagation. --- elastic wave. --- elasticity equation. --- elasticity imaging. --- elasticity. --- ellipse. --- energy functional. --- extended inclusion. --- extended source term. --- extended target. --- far-field measurement. --- filtered quadratic misfit. --- function space. --- gradient scheme. --- hard inclusion. --- hard inclusions. --- heterogeneous shear distribution. --- high contrast coefficient. --- hole. --- imaging functional. --- inclusion. --- incompressible limit. --- internal displacement measurement. --- layer potential. --- linear elasticity. --- linear transformation. --- linearized reconstruction problem. --- measurement noise. --- medium noise. --- nanoparticle. --- nonlinear optimization problem. --- nonlinear problem. --- operator-valued function. --- optimal control. --- potential energy functional. --- pressure. --- radiation condition. --- random fluctuation. --- resolution. --- reverse-time migration. --- scalar wave equation. --- search algorithm. --- shape change. --- shape deformation. --- shape. --- shear distribution. --- shear modulus. --- shear wave. --- small crack. --- small inclusion. --- small-volume expansion. --- small-volume inclusion. --- soft inclusion. --- stability analysis. --- stability. --- static regime. --- stochastic modeling. --- time-harmonic regime. --- time-reversal imaging. --- topological derivative. --- vibration testing.