International audienceIn this paper, we study Newton-type methods for solving generalized equations involving set-valued maps in Banach spaces. Kantorovich-type theorems (both local and global versions) are proved as well as the quadratic convergence of the Newton sequence. We also extend Smale's classical (α,γ)-theory to generalized equations. These results are new and can be considered as an extension of many known ones in the literature for classical nonlinear equations. Our approach is based on tools from variational analysis. The metric regularity concept plays an important role in our analysis

The article substantiates the relevance of the inspection of overhead power lines by determining the mechanical loads of the conductors. The conductor sways under the action of external loads and variable internal mechanical loads. The conductor behaves in span like a pendulum. A model of the harmonic oscillations of the conductor in flight is derived to assess the mechanical loads of the conductor overhead power lines. This mathematical model is based on mathematical models of a flexible thread and a model of a physical pendulum. A conductor is a physical pendulum, where the conductor acts as the body, and in the role of the fixed axis of rotation, a straight line passing through the suspension points of the conductor. The article briefly describes an algorithm for calculating the conductor sag for the case when the conductor suspension points are at the same height. The results obtained using the developed model for calculating the sag of the conductor by its period are compared with the available experimental data. Experimental equipment is described. The error of the method is estimated.

This paper presents a vibration-based structural health monitoring (SHM) technique for the identification of damage in a concrete arch beam replica section of the Sydney Harbour Bridge. The proposed technique uses residual frequency response functions (FRFs) combined with principal component analysis (PCA) to form a damage specific feature (DSF) that is used as an input parameter to artificial neural networks (ANNs). Extensive laboratory testing and numerical modelling are undertaken to validate the method. In the proposed technique, FRFs are obtained by the standard modal testing and damage is identified using ANNs that innovatively map the DSF to the severity of damage (length of damage cut). The results of the experimental and numerical validation show that the proposed technique can successfully quantify damage induced to a concrete arch beam simulating a real life structural component of the Sydney Harbour Bridge.

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