Abstract Summary
Aeroelastic stability is one of the main concerns in the design of long-span suspension bridges. According to the most widespread formulation, suspension bridges subjected to self-excited aerodynamic load represent a dynamic non-proportionally damped system where both damping and stiffness are affected by wind load and structural frequency. In this work, a one-dimensional (1D) continuum model for the multimodal aeroelastic analysis of suspension bridges is presented which refines a previous model presented by some of the authors. The equations governing the bridge vertical and torsional motion, based on the classical linearized theory, are enhanced to include the following wind-related geometric nonlinearities: the stiffness degradation induced by the upward lift and a Prandtl-like second order effect due to drag. For this purpose, the linearization of the equilibrium equations is made around the prestressed bridge configuration under the dead load and the mean steady drag and lift forces. The unsteady component of the wind load, defined via Scanlan’s flutter derivatives, is embedded as a self-excited perturbation of the prestressed system. According to the model, the coupling between vertical and torsional motion is triggered by the steady aerodynamic (often called “aerostatic”) component of the wind load, in addition to the coupling provided by the unsteady aerodynamic load already included in classical flutter theories. A multimode system is obtained by Galerkin’s method, where the vertical and torsional displacements are described as linear combinations of sinusoidal functions of the coordinate measured along the deck axis. A quadratic eigenvalue problem is thus obtained by the singularity check of the system matrix for each value of the reduced wind speed. Due to the interplay between the unsteady wind load and the oscillation frequencies of the system, an iterative procedure is adopted to find the solution and investigate equilibrium stability. The interpretation of the complex eigen-solution provides information about the evolution of the modal properties with increasing of wind speed. The real and imaginary parts of the complex eigenvalues represent the modal damping factors and angular frequencies, respectively. Besides, the complex eigenvectors contain information about the contribution of each sine function to the mode shapes and their temporal shift. In this way, the variation of the bridge mode shapes and frequencies under the wind load can be investigated; the instability condition is identified by the occurrence of a positive modal damping factor, in a classic Lyapunov framework. Numerical examples of coupled flutter and torsional flutter will be presented, providing a comparison of the results with literature data. The coupling between the two displacement components is highlighted as well as the interaction between different modes. Some peculiar aspects of the modal interaction as the curve veering of eigenvalue loci are investigated in terms of modal shape variation of different modal branches.
