Reconstructing blockages in a symmetric duct via quasi-isospectral horn operators

This paper proposes a new method for the reconstruction of the blockage area function in a symmetric duct by resonant frequencies under a given set of end conditions, i.e., open open or closed-closed ends. The analysis is based on the explicit determination of quasi-isospectral ducts, that is duct profiles which have the same spectrum as a given duct with the exception of a single eigenfrequency which is free to move in a prescribed interval. The analytical reconstruction was numerically implemented and tested for the detection of blockages. Numerical results show that the accuracy of identification increases with the number of eigenfrequencies used and that the reconstruction is rather stable with respect to the shape, the size and the position of the blockages

Numerical size estimates of inclusions in Kirchhoff-Love elastic plates

The size estimates approach for Kirchhoff--Love elastic plates allows to determine upper and lower bounds of the area of an unknown elastic inclusion by measuring the work developed by applying a couple field on the boundary of the plate. Although the analytical process by which such bounds are determined is of constructive type, it leads to rather pessimistic evaluations. In this paper we show by numerical simulations how to obtain such bounds for practical applications of the method. The computations are developed for a square plate under various boundary loads and for inclusions of different position, shape and stiffness. The sensitivity of the results with respect to the relevant parameters is also analyzed

Resonator-based detection in nanorods

In this paper the axial vibrational behaviour of nanorods with an attached point-mass is studied, using the modified strain energy theory. The natural frequencies of the nanorod with the concentrated mass are obtained for different boundary conditions. The effects of the concentrated mass intensity, mass location, as well as the value of scale parameters have been analysed. For the case of small intensity of the concentrated mass, the natural frequencies of the nanorod can be estimated using a first order perturbative solution. These approximate results are compared with those corresponding to the exact solution. For this case, from the properties of the eigenvalue perturbative theory, the identification of single point mass in uniform nanorods (mass intensity and position) is addressed. The results obtained encourage the use of axial vibrations of nanorods as a very precise sensing technique

Explicit Determination of Pinned-Pinned Beams with a Finite Number of Given Buckling Loads

We present an analytical procedure for the exact, explicit construction of Euler-Bernoulli beams with given values of the first N buckling loads. The result is valid for pinned-pinned (P-P) end conditions and for beams with regular bending stiffness. The analysis is based on a reduction of the buckling problem to an eigenvalue problem for a vibrating string, and uses recent results on the exact construction of Sturm-Liouville operators with prescribed natural frequencies

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples

Clinical, Radiographic, Histopathologic, and Serologic Features and their Differentiation from Wegener Granulomatosis

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Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure