Quasi-isospectral Sturm-Liouville operators and applications to system identification

Abstract 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

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

A MATLAB-Based Symbolic Approach for the Quick Developing of Nonlinear Solid Mechanics Finite Elements

A symbolic mathematical approach for the rapid early phase developing of finite elements is proposed. The algebraic manipulator adopted is MATLAB® and the applicative context is the analysis of hyperelastic solids or structures under the hypothesis of finite deformation kinematics. The work has been finalized through the production, in an object-oriented programming style, of three MATLAB® classes implementing a truss element, a tetrahedral element and plane element. The approach proposed, starting from the mathematical formulation and finishing with the code implementation, is described and its effectiveness, in terms of minimization of the gap between the theoretical formulation and its actual implementation, is highlighted

NONLINEAR ANALYSIS OF BRITTLE MATERIALS

The problem of the evaluation of the nonlinear response of damaged structures is considered. In order to circumvent the numerical difficulties which can affect standard numerical strategies because of the high sensitivity of the stress response to small changes of displacements, a specific implementation of the standard path–following procedure is presented. The approach is based on a parametrization of the equilibrium curve which takes into account also the variables used in the modelling of the damage process. Two damage models, an isotropic one and an orthotropic one, are implemented in order to verify the numerical procedure in the analysis of 2D continua subjected to plane stress condition

NONLINEAR ANALYSIS OF BRITTLE MATERIALS

The problem of the evaluation of the nonlinear response of damaged structures is considered. In order to circumvent the numerical difficulties which can affect standard numerical strategies because of the high sensitivity of the stress response to small changes of displacements, a specific implementation of the standard path–following procedure is presented. The approach is based on a parametrization of the equilibrium curve which takes into account also the variables used in the modelling of the damage process. Two damage models, an isotropic one and an orthotropic one, are implemented in order to verify the numerical procedure in the analysis of 2D continua subjected to plane stress condition

STRUCTURAL FIRE SAFETY OF EXISTING STEEL BUILDINGS, Possible general approach and application to the case of the intumescent coatings

The fire safety of the existing structures is very important from the socio-economic point of view and has high social impact for civil, industrial, and commercial buildings. The verification of the minimum fire resistance of civil structures is done through some regulations, drafted to ensure occupant and rescue teams safety as well as a limited structural damage. These national fire rules are not always easily applicable to existing buildings. The purpose of this paper is to provide guidance about the structural analysis of existing buildings exposed to fire, with particular reference to steel buildings protected with intumescent coatings