Gian Felice Giaccu

Asymptotics of eigenfrequencies in the dynamic response of elongated multi-structures

The paper addresses a mathematical model describing the dynamic response of an elongated bridge supported by elastic pillars. The elastic system is considered as a multi-structure involving subdomains of different limit dimensions connected via junction regions. Analytical formulae have been derived to estimate eigenfrequencies in the low frequency range. The analytical findings for Bloch–Floquet waves in an infinite periodic structure are compared with the finite element numerical computations for an actual bridge structure of finite length. The asymptotic estimates obtained here have also been used as a design tool in problems of asymptotic optimization.

Parametric Study on the Nonlinear Dynamics of a Three-Stay Cable Network under Stochastic Free Vibration

AbstractCrossties and cable networks are used on cable-stayed bridges to mitigate wind-induced stay vibration. A nonlinear free-vibration analysis of a cable network with random oscillation amplitudes is presented in this study. Specifically, a nonlinear restoring-force spring model is introduced at the crosstie to simulate in-plane network free vibration at large amplitudes. The current constitutive model of the crosstie is also combined with taut-cable theory to simulate the dynamics in the stays and is solved by the equivalent linearization method. Stochastic functions are introduced in the model because the measure of the amplitudes produced by wind- and rain-wind–induced vibrations in the network can be affected by various uncertainties. The stochastic approximation (SA) algorithm is applied to find the roots of the characteristic polynomials associated with a stochastic vibration amplitude parameter. Brute force Monte Carlo methods are also used to analyze the SA convergence properties.

Transition wave in the collapse of the San Saba Bridge

A domino wave is a well-known illustration of a transition wave, which appears to reach a stable regime of propagation. Nature also provides spectacular cases of gravity driven transition waves at large scale, observed in snow avalanches and landslides. On a different scale, the micro-structure level interaction between different constituents of the macro-system may influence critical regimes leading to instabilities in avalanche-like flow systems. Most transition waves observed in systems such as bulletproof vests, racing helmets under impact, shock-wave driven fracture in solids, are transient. For some structured waveguides a transition wave may stabilize to achieve a steady regime. Here we show that the failure of a long bridge is also driven by a transition wave that may allow for steady-state regimes. The recent observation of a failure of the San Saba Bridge in Texas provides experimental evidence supporting an elegant theory based on the notion of transition failure wave. No one would think of an analogy between a snow avalanche and a collapsing bridge. Despite an apparent controversy of such a comparison, these two phenomena can both be described in the framework of a model of the dynamic gravity driven transition fault.

Dynamic multi-structure in modelling a transition flexural wave

This paper presents a model of a 1D–1D dynamic multi-structure, supporting propagation of a transition wave. It is used to explain the recent phenomenon of the collapse of the San Saba bridge. An analytical model is supplied with illustrative numerical simulations.

Dynamics of Strongly Curved Concrete Beams by Isogeometric Finite Elements

The standard finite elements approach for the dynamics of curved beam is usually based on the same energy functional used for straight beam, in other words an energy form that is essentially derived from de Saint–Venant’s theory. In case of strongly curved elements this approximation yields to not negligible errors, in particular for stress assessments. For this reason, in this work a different formulation, based on the Winkler’s simple kinematic assumptions, is adopted. In this way a non diagonal constitutive matrix is obtained and the computational efficiency of NURBS (Non Uniform Rational B–Splines) shape functions is added to an accurate representation of the constitutive relations. In this paper the natural frequencies and mode shapes of plane curved concrete beams are obtained. Computational cost and results accuracy is assessed with respect to closed form solutions and literature results.