Vibration Testing

2015 ◽  
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  
Keyword(s):  
Integral Representations ◽  
Asymptotic Formulas ◽  
Vibration Testing ◽  
Linear Elastic ◽  
Damage Location ◽  
Characteristic Values ◽  
Elastic Inclusions ◽  
Complex Planes ◽  
Shape Changes ◽  
Shape Deformations

This chapter deals with vibration testing, which aims to identify inclusions, cracks, or shape changes in a structure by measuring its modal characteristics. The measured eigenparameters are related to the defect or damage location, orientation, and size. The chapter derives asymptotic formulas for eigenvalue perturbations due to small inclusions, cracks, and shape deformations. The main ingredients in deriving the results are the integral equations and the theory of meromorphic operator-valued functions. Using integral representations of solutions to the harmonic oscillatory linear elastic equation, this problem is reduced to the study of characteristic values of integral operators in the complex planes. The chapter focuses on three kinds of elastic inclusions: holes, hard inclusions, and soft inclusions.

Linear elastic eigenstates of the compliance tensor for trigonal crystals

2000 ◽  
Vol 215 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P.S. Theocaris ◽  
D.P. Sokolis
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Symmetric Tensor ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Trigonal System ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Strain Tensors ◽  
Elastic Strain Energy Density

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

Introduction

2015 ◽  
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  
Keyword(s):  
Optimal Control ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Stochastic Modeling ◽  
Physical Parameters ◽  
Vibration Testing ◽  
Elastic Structures ◽  
Modeling And Analysis ◽  
Elastic Inclusions ◽  
Statistical Approaches

This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers important developments in asymptotic imaging, stochastic modeling, and analysis of both deterministic and stochastic elastic wave propagation phenomena and puts them together in a coherent way. It gives emphasis on deriving the best possible imaging functionals for small inclusions and cracks in the sense of stability and resolution. For imaging extended elastic inclusions, the book develops accurate optimal control methodologies and examines the effect of uncertainties of the geometric or physical parameters on their stability and resolution properties. It also presents an asymptotic framework for vibration testing and a method for identifying, locating, and estimating inclusions and cracks in elastic structures by measuring their modal characteristics.

Swimming due to transverse shape deformations

2009 ◽  
Vol 631 ◽  
pp. 127-148 ◽  
Author(s):  
EVA KANSO
Keyword(s):  
Potential Flow ◽  
Deformable Body ◽  
Three Dimensional ◽  
Point Vortices ◽  
Vortex Wake ◽  
Balance Laws ◽  
Reactive Force ◽  
Slender Bodies ◽  
Shape Changes ◽  
Shape Deformations

Balance laws are derived for the swimming of a deformable body due to prescribed shape changes and the effect of the wake vorticity. The underlying balances of momenta, though classical in nature, provide a unifying framework for the swimming of three-dimensional and planar bodies and they hold even in the presence of viscosity. The derived equations are consistent with Lighthill's reactive force theory for the swimming of slender bodies and, when neglecting vorticity, reduce to the model developed in Kanso et al. (J. Nonlinear Sci., vol. 15, 2005, p. 255) for swimming in potential flow. The locomotion of a deformable body is examined through two sets of examples: the first set studies the effect of cyclic shape deformations, both flapping and undulatory, on the locomotion in potential flow while the second examines the effect of the wake vorticity on the net locomotion. In the latter, the vortex wake is modelled using pairs of point vortices shed periodically from the tail of the deformable body.

scholarly journals Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Rauf Kh. Amırov ◽  
A. Adiloglu Nabıev
Keyword(s):  
Inverse Problems ◽  
Boundary Value Problem ◽  
Finite Interval ◽  
Boundary Value ◽  
Weyl Function ◽  
Integral Representations ◽  
Asymptotic Formulas ◽  
Linearly Independent ◽  
Quadratic Pencil ◽  
Sturm Liouville

In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.

scholarly journals Mean time for the development of large workloads and large queue lengths in the GI/G/1 queue

1996 ◽  
Vol 9 (2) ◽  
pp. 107-142
Author(s):  
Charles Knessl ◽  
Charles Tier
Keyword(s):  
Integral Representations ◽  
Kolmogorov Equation ◽  
Asymptotic Formulas ◽  
Asymptotic Results ◽  
Singular Perturbation Analysis ◽  
Queue Lengths ◽  
The Mean ◽  
Number Of Customers ◽  
Mean Time ◽  
Passage Times

We consider the GI/G/1 queue described by either the workload U(t) (unfinished work) or the number of customers N(t) in the system. We compute the mean time until U(t) reaches excess of the level K, and also the mean time until N(t) reaches N0. For the M/G/1 and GI/M/1 models, we obtain exact contour integral representations for these mean first passage times. We then compute the mean times asymptotically, as K and N0→∞, by evaluating these contour integrals. For the general GI/G/1 model, we obtain asymptotic results by a singular perturbation analysis of the appropriate backward Kolmogorov equation(s). Numerical comparisons show that the asymptotic formulas are very accurate even for moderate values of K and N0.

scholarly journals Chronic exposure to haloperidol and olanzapine leads to common and divergent shape changes in the rat hippocampus in the absence of grey-matter volume loss

2016 ◽  
Vol 46 (15) ◽  
pp. 3081-3093 ◽  
Author(s):  
W. R. Crum ◽  
F. Danckaers ◽  
T. Huysmans ◽  
M.-C. Cotel ◽  
S. Natesan ◽  
...  
Keyword(s):  
Chronic Exposure ◽  
Hippocampal Volume ◽  
Rat Hippocampus ◽  
Shape Deformation ◽  
Deformation Analysis ◽  
Grey Matter Volume ◽  
Post Mortem ◽  
True Shape ◽  
Shape Changes ◽  
Shape Deformations

BackgroundOne of the most consistently reported brain abnormalities in schizophrenia (SCZ) is decreased volume and shape deformation of the hippocampus. However, the potential contribution of chronic antipsychotic medication exposure to these phenomena remains unclear.MethodWe examined the effect of chronic exposure (8 weeks) to clinically relevant doses of either haloperidol (HAL) or olanzapine (OLZ) on adult rat hippocampal volume and shape using ex vivo structural MRI with the brain retained inside the cranium to prevent distortions due to dissection, followed by tensor-based morphometry (TBM) and elastic surface-based shape deformation analysis. The volume of the hippocampus was also measured post-mortem from brain tissue sections in each group.ResultsChronic exposure to either HAL or OLZ had no effect on the volume of the hippocampus, even at exploratory thresholds, which was confirmed post-mortem. In contrast, shape deformation analysis revealed that chronic HAL and OLZ exposure lead to both common and divergent shape deformations (q = 0.05, FDR-corrected) in the rat hippocampus. In particular, in the dorsal hippocampus, HAL exposure led to inward shape deformation, whereas OLZ exposure led to outward shape deformation. Interestingly, outward shape deformations that were common to both drugs occurred in the ventral hippocampus. These effects remained significant after controlling for hippocampal volume suggesting true shape changes.ConclusionsChronic exposure to either HAL or OLZ leads to both common and divergent effects on rat hippocampal shape in the absence of volume change. The implications of these findings for the clinic are discussed.

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