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

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

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

Reconstructing Loads in Nanoplates from Dynamic Data

It was recently proved that the knowledge of the transverse displacement of a nanoplate in an open subset of its mid-plane, measured for any interval of time, allows for the unique determination of the spatial components (Formula presented.) of the transverse load (Formula presented.), where (Formula presented.) and (Formula presented.) is a known set of linearly independent functions of the time variable. The nanoplate mechanical model is built within the strain gradient linear elasticity theory, according to the Kirchhoff–Love kinematic assumptions. In this paper, we derive a reconstruction algorithm for the above inverse source problem, and we implement a numerical procedure based on a finite element spatial discretization to approximate the loads (Formula presented.). The computations are developed for a uniform rectangular nanoplate clamped at the boundary. The sensitivity of the results with respect to the main parameters that influence the identification is analyzed in detail. The adoption of a regularization scheme based on the singular value decomposition turns out to be decisive for the accuracy and stability of the reconstruction

On Isospectral Composite Beams

We consider a composite system consisting of two identical straight elastic beams under longitudinal vibration connected by an elastic interface capable of counteracting the relative vibration of the two beams with its shearing stiffness. We construct examples of isospectral composite beams, i.e., countable one-parameter families of beams having different shearing stiffness but exactly the same eigenvalues under a given set of boundary conditions. The construction is explicit and is based on the reduction to a one-dimensional Sturm–Liouville eigenvalue problem and the application of a Darboux’s lemma

Influence of structural irregularity on the q-behaviour factor of light-frame timber buildings by means of incremental dynamic analysis

This paper investigates the role of sheathing-to-framing connection ductility in the evaluation of the structural q-behaviour factor for Light-Frame Timber (LFT) buildings, by means of Incremental Dynamic Analyses (IDA). This approach allows to consider nonlinear cyclic behaviour of the walls, which cannot be taken into account with the static approaches used in most of the available literature on LFT buildings. To this aim, Finite Element wall models, preliminary calibrated towards a cyclic full-scale experimental test, are built to study six case-study buildings, both regular and non-regular, with 2, 3 or 4 storeys, which were designed according to Eurocode and Capacity Design provisions. Parametric analyses are performed by varying the displacement-ductility of the panel. Finally, numerical results are discussed in terms of q-behaviour factor, and its sensitivity to structural irregularities, with respect to existing code provisions for timber buildings

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Stable determination of the Winkler subgrade coefficient in a nanoplate

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff-Love kinematic assumptions in infinitesimal deformation. We prove a global Hölder stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point

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