Papers by Antonino Morassi
Journal of Structural Engineering, 2010
This paper continues a line of research aimed at the development of a dynamically based health co... more This paper continues a line of research aimed at the development of a dynamically based health condition monitoring of bridge structures in the area of Friuli Venezia Giulia, Italy. One subject of this research program has been a two-span highway bridge with a concrete slab supported by closely spaced precast beams, a constructive typology which is quite diffuse in the regional highway network. Forced-vibration tests and experimental modal analysis were used to determine the vibration properties of the structure. An identification procedure based on dynamic data allowed to define an accurate orthotropic plate model of the deck and to improve the description of some constructional details in the finite-element model of the bridge such as the boundary conditions on abutments and the connection between the deck and pier. The usefulness of the combined experimental and analytical process in the identification of structural properties has been proven and the procedure can be applied to other structures of the same typology.
International Journal of Solids and Structures, Mar 1, 2013
Localized flexibility models of cracks enable one for simple and effective representation of the ... more Localized flexibility models of cracks enable one for simple and effective representation of the behavior of damaged beams and frames. Important applications, such as the determination of closed-form solutions and the development of diagnostic methods of analysis have attracted the interest of many researchers in recent years. Nevertheless, certain fundamental questions have not been completely clarified yet. One of these issues concerns with the mechanical justification of the macroscopic model of rotational elastic spring commonly used to describe the presence of an open crack in a beam under bending deformation. Two main analytical formulations have been recently proposed to take into account the singularity generated by the crack. The crack is represented by suitable Dirac's delta functions either in the beam's flexural rigidity or in the beam's flexural flexibility. Both approaches require some caution due to mathematical subtleties of the analysis. Motivated by these considerations, in this paper we propose a justification of the rotational elastic spring model of an open crack in a beam in bending deformation. We show that this localized flexibility model of a crack is the variational limit of a family of one-dimensional beams when the flexural stiffness of these beams tends to zero in an interval centered at the cracked cross-section and, simultaneously, the length of the interval vanishes in a suitable way. We also show that the static and dynamic problem for the flexibility model of cracked beam can be formulated within the classical context of the theory of distributions, avoiding the hindrances encountered in previous approaches to the problem. In addition, the proposed treatment leads to a simple and efficient determination of exact closed form solutions of both static and dynamic problems for beams with multiple cracks.
Structural control & health monitoring, May 30, 2018
In this work a model of the Euler-Bernoulli beam in presence of multiple concentrated open cracks... more In this work a model of the Euler-Bernoulli beam in presence of multiple concentrated open cracks, based on the adoption of a localized flexibility model, is adopted. The closed form solution in terms of transversal displacements due to static loads and general boundary condition is exploited to propose an inverse damage identification procedure. The proposed identification procedure does not require any solution algorithm, on the contrary is formulated by means of simple explicit sequential expressions for the crack positions and intensities including the identification of the integration constants. The number of possible detected cracks depends on the couples of adopted sensors. Undamaged beam zones can also be easily detected in relation to the sensor positions. The analytical character of the explicit expressions of the identification procedure makes the inverse formulation applicable to damaged beams included in more complex frame structures. The proposed procedure is applied for the identification of the number, position and intensity of the cracks along simple straight beams and also to more complex frame structures with the aim of showing its simplicity for engineering applications. In addition, the robustness of the methodology here described is shown through an accurate analysis of the basic assumptions on which the theory relies, and by means of a study of the effect of noise on the identification results.
Mechanical Systems and Signal Processing, Sep 1, 2017
In this paper the axial vibrational behaviour of nanorods with an attached point-mass is studied,... more 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.
Forum Mathematicum, 2008
We investigate the character of the linear constraints which are needed for Poincaré and Korn typ... more We investigate the character of the linear constraints which are needed for Poincaré 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.
arXiv (Cornell University), Sep 26, 2012
In this paper we review some recent results concerning inverse problems for thin elastic plates. ... more In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by nonhomogeneous linearly elastic material belonging to a general class of anisotropy. A first group of results concerns uniqueness and stability for the determination of unknown boundaries, including the cases of cavities and rigid inclusions. In the second group of results, we consider upper and lower estimates of the area of unknown inclusions given in terms of the work exerted by a couple field applied at the boundary of the plate. In particular, we extend previous size estimates for elastic inclusions to the case of cavities and rigid inclusions.
Applicable Analysis, Mar 27, 2020
We derive upper and lower estimates of the area of unknown defects in the form of either cavities... more We derive upper and lower estimates of the area of unknown defects in the form of either cavities or rigid inclusions in Mindlin-Reissner elastic plates in terms of the difference δW of the works exerted by boundary loads on the defected and on the reference plate. It turns out that the upper estimates depend linearly on δW , whereas the lower ones depend quadratically on δW. These results continue a line of research concerning size estimates of extreme inclusions in electric conductors, elastic bodies and plates.
arXiv (Cornell University), Oct 5, 2016
In this paper we consider the stability issue for the inverse problem of determining an unknown i... more In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the body and the inclusion are made by inhomogeneous linearly elastic isotropic material. Under mild a priori assumptions about the smoothness of the inclusion and the regularity of the coefficients, we show that the logarithmic stability estimate proved in [A-DiC-M-R] in the case of piecewise constant coefficients continues to hold in the inhomogeneous case. We introduce new arguments which allow to simplify some technical aspects of the proof given in [A-DiC-M-R].
Communications in Partial Differential Equations, Sep 1, 2001
We prove quantitative estimates of unique continuation for the solutions of the Lamé system of th... more We prove quantitative estimates of unique continuation for the solutions of the Lamé system of the form of three–spheres–inequalities and of doubling inequalities. Work supported in part by MURST and by CNR.
arXiv (Cornell University), Sep 19, 2022
We consider the problem of determining, within an elastic isotropic nanoplate in bending, the pos... more We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide quantitative upper and lower estimates for the area of the unknown defect in terms of the works exerted by the boundary data when the inclusion
Journal of Sound and Vibration, Jun 1, 2016
In this paper we consider one of the basic inverse problems in damage detection based on natural ... more In this paper we consider one of the basic inverse problems in damage detection based on natural frequency data, namely the identification of a single open crack in a uniform simply supported beam from measurement of the first and the second natural frequency. It is commonly accepted in the literature that the knowledge of this set of spectral data allows for the unique determination of the severity and the position (up to symmetry) of the damage. However, in spite of the fact that many numerical evidences are in support of this property, the result is rigorously proved only when the severity of the crack is small. In this paper we definitely show, by means of an original constructive method, that the above result holds true for any level of crack severity.
Journal of Vibration and Control, Jul 8, 2013
In this paper an analytical, exact procedure for the reconstruction of simply supported bending v... more In this paper an analytical, exact procedure for the reconstruction of simply supported bending vibrating beams having given values of the first N natural frequencies is presented. The results hold for beams in which the product between the bending stiffness and the linear mass density is constant. The analysis is based on the fact that this class of beams is spectrally equivalent to a family of strings fixed at the ends, and uses recent results on the exact construction of second-order Sturm–Liouville operators with prescribed natural frequencies. The analysis can be adapted to beams with pinned–sliding and sliding–sliding ends.
Vibroengineering Procedia
This paper investigates the role of sheathing-to-framing connection ductility in the evaluation o... more 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.
Journal of Engineering Mechanics-asce, May 1, 1997
Most of the diagnostic techniques via modal analysis are based on an optimality criterion where t... more Most of the diagnostic techniques via modal analysis are based on an optimality criterion where the stiffness distribution of a chosen reference configuration of the structural system is updated so that the first few natural frequencies closely match the measured ones at a certain level of deterioration. Despite the common use of these techniques in damage identification, basic questions such as how accurate the reference configuration has to be or which \Ia priori\N hypotheses are needed to get around the badly posed diagnostic problem are unclear and still open. In this paper a diagnostic strategy for identifying a localized damage in a multistory steel frame is discussed, with an eye to these questions and to practical use of vibration monitoring on field measurements. It was found that the dynamic characterization of the frame at a certain stage of its service is indispensable to defining an accurate analytical model of the structure, that is, to defining a reference configuration of the frame that is useful for identifying possible incremental damages. Moreover, some working hypotheses commonly used in structural diagnostics were found to be crucial in reducing the indeterminacy of the identification problem. The obtained results essentially confirm a more careful resolution on the localization of the damage as its severeness increases.
Structural Engineering and Mechanics, 2001
Structural identification via modal analysis in structural mechanics is gaining popularity in rec... more Structural identification via modal analysis in structural mechanics is gaining popularity in recent years, despite conceptual difficulties connected with its use. This paper is devoted to illustrate both the capabilities and the indeterminacy characterizing structural identification problems even in quite simple instances, as well as the cautions that should be accordingly adopted. In particular, we discuss an application of an identification technique of variational type, based on the measurement of eigenfrequencies and mode shapes, to a steel frame with friction joints under various assembling conditions. Experience has suggested, so as to restrict the indeterminacy frequently affecting identification issues, having resort to all the a priori acknowledged information on the system, to the symmetry and presence of structural elements with equal stiffness, to mention one example, and mindfully selecting the parameters to be identified. In addition, considering that the identification techniques have a local character and correspond to the updating of a preliminary model of the structure, it is important that the analytical model on the first attempt should be adequately accurate. Secondly, it has proved determinant to cross the results of the dynamic identification with tests of other typology, for instance, static tests, so as to fully understand the structural behavior and avoid the indeterminacy due to the nonuniqueness of the inverse problem.
CISM International Centre for Mechanical Sciences, 2008
CISM International Centre for Mechanical Sciences, 2008
WIT transactions on engineering sciences, 1998
This paper is an analytical/experimental investigation of the effect of damage on the nodes of fr... more This paper is an analytical/experimental investigation of the effect of damage on the nodes of free vibration modes of a thin rod in longitudinal vibration. The damage, a notch, is simulated by a simple spring. It is shown that nodes move towards the notch. The direction and amount by which they move may be used to estimate the position and severity of the damage Analytical results agree well with experimental tests.
Procedia Engineering, 2017
Quasi-isospectral Sturm-Liouville operators play an important role in inverse spectral theory and... more Quasi-isospectral Sturm-Liouville operators play an important role in inverse spectral theory and are typically used for determining exact solutions to suitable classes of eigenvalue problems with variable coefficients. In this work we investigate on alternative applications of quasi-isospectral operators as key tool for structural identification purposes. We review some recent results concerned with the construction of rods with a given finite number of natural frequencies and we present some generalization to beams under bending vibration and to the identification of damages from natural frequency data. c
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Papers by Antonino Morassi