Aeroelastic instability induced by wind loads is one of the main concerns in the design of long-span suspension bridges. The increasing length of the main span - the recent 1915 Canakkale Bridge in Turkey established a new World record with its central span of 2023 m - and the consequent increase in flexibility makes these bridges highly sensitive to the wind action. Since the Tacoma Narrows Bridge failure of 1940, several semi-analytic, semi-empirical methods have been proposed to describe the aeroelastic behaviour of suspension bridges in order to predict the stability threshold. In this talk, an enhancement of a linear semi-analytic continuum model previously proposed by two of the authors for the dynamic aeroelastic analysis of suspension bridges will be presented. In compliance with the linearised deflection theory of suspension bridges, the kinematics of the bridge cross-section is described by means of two displacement parameters: the vertical deflection of the deck cross-section and its torsion rotation. The latter parameters are functions of the centroidal longitudinal coordinate of the bridge deck (coinciding with the elastic axis), allowing to describe the deck deformation by a one-dimensional structural model. The Scanlan’s definition of the aeroelastic lift and moment by means of flutter derivatives is adopted, whereas the contribution of the mean steady drag force is embedded as a Prandtl-like second-order effect. The additional second-order terms introduced, depict distributed vertical and torsion loads arising from a change in the geometric configuration of the system, thus, a form of geometric nonlinearity. A multi-degree-of-freedom model is thus obtained from the two partial integro-differential equations governing the flexural-torsional motion by Galerkin’s method, defining the vertical and torsional kinematic parameters as weighted sums of sinusoidal functions. An iterative procedure is introduced to carry out the eigenvalue analysis of the self-excited system for increasing wind speeds. The bridge modal frequencies are depicted by the imaginary parts of the complex eigenvalues while the real parts represent the modal damping factors. The variation of the eigenvalues with the wind load is investigated, as well as the evolution of the corresponding modal shapes, these latter being described by the real and imaginary components of the eigenvectors. The effect of the steady drag force on the flexural-torsional aeroelastic behaviour is highlighted and shown to be an affective coupling feature between the degrees of freedom. Divergence and flutter aeroelastic instabilities are identified by the appearance of eigenvalues having a non-negative real part and zero or positive imaginary part, respectively. Numerical examples will be presented, providing a comparison of the results with those of the literature and of Finite Element analyses.

Linear aeroelastic analysis of suspension bridges with second-order effects / Russo, Sebastiano; Piana, Gianfranco; Carpinteri, Alberto. - ELETTRONICO. - (2022), pp. 34-34. (Intervento presentato al convegno ICCSE2 2nd International Conference on Computations for Science and Engineering tenutosi a Rimini Riviera (Italy) nel 30 August - 2 September 2022).

### Linear aeroelastic analysis of suspension bridges with second-order effects

#### Abstract

Aeroelastic instability induced by wind loads is one of the main concerns in the design of long-span suspension bridges. The increasing length of the main span - the recent 1915 Canakkale Bridge in Turkey established a new World record with its central span of 2023 m - and the consequent increase in flexibility makes these bridges highly sensitive to the wind action. Since the Tacoma Narrows Bridge failure of 1940, several semi-analytic, semi-empirical methods have been proposed to describe the aeroelastic behaviour of suspension bridges in order to predict the stability threshold. In this talk, an enhancement of a linear semi-analytic continuum model previously proposed by two of the authors for the dynamic aeroelastic analysis of suspension bridges will be presented. In compliance with the linearised deflection theory of suspension bridges, the kinematics of the bridge cross-section is described by means of two displacement parameters: the vertical deflection of the deck cross-section and its torsion rotation. The latter parameters are functions of the centroidal longitudinal coordinate of the bridge deck (coinciding with the elastic axis), allowing to describe the deck deformation by a one-dimensional structural model. The Scanlan’s definition of the aeroelastic lift and moment by means of flutter derivatives is adopted, whereas the contribution of the mean steady drag force is embedded as a Prandtl-like second-order effect. The additional second-order terms introduced, depict distributed vertical and torsion loads arising from a change in the geometric configuration of the system, thus, a form of geometric nonlinearity. A multi-degree-of-freedom model is thus obtained from the two partial integro-differential equations governing the flexural-torsional motion by Galerkin’s method, defining the vertical and torsional kinematic parameters as weighted sums of sinusoidal functions. An iterative procedure is introduced to carry out the eigenvalue analysis of the self-excited system for increasing wind speeds. The bridge modal frequencies are depicted by the imaginary parts of the complex eigenvalues while the real parts represent the modal damping factors. The variation of the eigenvalues with the wind load is investigated, as well as the evolution of the corresponding modal shapes, these latter being described by the real and imaginary components of the eigenvectors. The effect of the steady drag force on the flexural-torsional aeroelastic behaviour is highlighted and shown to be an affective coupling feature between the degrees of freedom. Divergence and flutter aeroelastic instabilities are identified by the appearance of eigenvalues having a non-negative real part and zero or positive imaginary part, respectively. Numerical examples will be presented, providing a comparison of the results with those of the literature and of Finite Element analyses.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2977928`