The linear constraints in Poincar\'{e} and Korn type inequalities

We investigate the character of the linear constraints which are needed for Poincar\'e and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a portion of the boundary.Comment: Revised versio

On doubling inequalities for elliptic systems

We prove doubling inequalities for solutions of elliptic systems with an iterated Laplacian as diagonal principal part and for solutions of the Lame' system of isotropic linearized elasticity. These inequalities depend on global properties of the solutions.Comment: 13 pages, submitted for publicatio

Uniqueness in the determination of loads in multi-span beams and plates

Most of the results available on the inverse problem of determining loads acting on elastic beams or plates under transverse vibration refer to single beam or single plate. In this paper, we consider the determination of sources in multi-span systems obtained by connecting either two Euler-Bernoulli elastic beams or two rectangular Kirchhoff-Love elastic plates. The material of the structure is assumed to be homogeneous and isotropic. The transverse load is of the form g(t)f(x), where g(t) is a known function of time and f(x) is the unknown term depending on the position variable x. Under slight a priori assumptions, we prove a uniqueness result for f(x) in terms of observations of the dynamic response taken at interior points of the structure in an arbitrary small interval of time. A numerical implementation of the method is included to show the possible application of the results in the practical identification of the source term

Stable determination of an inclusion in an elastic body by boundary measurements (unabridged)

We consider the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material. The Lam\'e moduli of the inclusion are constant and different from those of the surrounding material. Under mild a-priori regularity assumptions on the unknown defect, we establish a logarithmic stability estimate. For the proof, we extend the approach used for electrical and thermal conductors in a novel way. Main tools are propagation of smallness arguments based on three-spheres inequality for solutions to the Lam\'e system and refined local approximation of the fundamental solution of the Lam\'e system in presence of an inclusion.Comment: 58 pages, 4 figures. This is the extended, and revised, version of a paper submitted for publication in abridged for

Crack detection in elastic beams by static measurements

AbstractThis paper deals with the identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the beam. The crack is simulated by an equivalent linear spring connecting the two adjacent segments of the beam. Sufficient conditions on static measurements which allow for the unique identification of the crack are presented and discussed. The inverse analysis provides exact closed-form expressions of position and severity of the crack as functions of deflection measurements for different boundary conditions. The theoretical results are confirmed by a comparison with static measurements on steel beams with a crack. Extension of the presented analysis to multiple cracks is briefly discussed

Experimental verification of the interpolation method on a real damaged bridge

The identification of damage in a bridge from changes in its vibrational behavior is an inverse problem of important practical value. Significant advances have been obtained on this topic in the last two-three decades, both from the theoretical and applied point of view. One of the main problems when dealing with the assessment of vibration based damage identification methods is the lack of experimental data recorded on real damaged structures. Due to this, a large number of damage identification algorithms are tested using data simulated by numerical models. The availability of data recorded on a damaged bridge before its demolition gave the authors the uncommon chance to verify the sensitivity and reliability of the IDDM basing on data recorded on a real structure. Specifically data recorded on a reinforced concrete single-span supported bridge in the Municipality of Dogna (Friuli, Italy) were used to apply the damage localization algorithm. Harmonically forced tests were conducted after imposing artificial, increasing levels of localized damage. In this paper the sensitivity of the method is discussed with respect to the number of instrumented locations and to the severity of the damage scenarios considere

The use of quasi-isospectral operators for damage detection in rods

We consider the inverse problem of reconstructing the axial stiffness of a damaged rod from the knowledge of a finite number of resonant frequencies of the free axial vibration under supported end conditions. The damage is described as a reduction of the axial stiffness, and the undamaged and damaged configurations of the rod are assumed to be symmetric. The method is based on repeated determination of quasi-isospectral rod operators, that is rods which have the same spectrum of a given rod with the exception of a single resonant frequency which is free to move in a prescribed interval. The reconstruction procedure is explicit and it is numerically implemented and tested for the identification of single and multiple localized damages. The sensitivity of the technique to the number of frequencies used and to the shape, intensity and position of the damages, as well as to the presence of noise in the data, is evaluated and discussed. The effect of suitable filtering of the results based on a priori information on the physics of the problem is proposed. An experimental application to the identification of localized damage in a free-free steel rod is also presented

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 -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