Nonlinear indicial functions for modelling aeroelastic forces of bluff bodies

Abstract

This study introduces a novel time-domain model of nonlinear indicial functions to capture the amplitude dependency of self-excited forces in aeroelastic instabilities, including flutter, vortex-induced vibration (VIV), and unsteady galloping. The model aims to reproduce the nonlinear aerodynamic forces that arise from large amplitude oscillations causing variations in the transient wind angle of attack. The model assumes that the decay coefficients in the indicial functions can be taken as nonlinear functions of the transient angle of attack induced by the body motion, enabling the incorporation of both amplitude dependency and memory effect within a simple time domain model. The proposed model is experimentally validated considering an unsteady galloping test of an elastically supported rectangular 2:1 cylinder sectional model. Keywords: aerodynamic nonlinearities; time domain model; nonlinear indicial functions; aerodynamic transfer functions; limit cycle oscillation aeroelastic instabilities, such as the linear flutter derivative model by Scanlan and Tomko [6-7], the Glauert-Den Hartog criterion for galloping instability [3], and the linear VIV model [1].However, a nonlinear model is required to accurately predict the transient responses, especially the stable amplitudes of LCOs [3][4][5][8][9][10][11][12][13][14].Existing self-excited models incorporating aerodynamic nonlinearity and unsteadiness can be broadly classified into two categories. The first type is expressed in a hybrid time-frequency domain using the concept of amplitude-dependent flutter derivatives [15][16][17] (also referred as "describing function model" by Zhang et al [11]). These models assume that the aerodynamic coefficients are frequency dependent to model the aerodynamic unsteadiness. They also employ a polynomial function of vibration amplitude to account for aerodynamic nonlinearity.Many semi-empirical nonlinear models can be reduced to a nonlinear amplitude-dependent flutter-derivative model [4-5, 8-12,16-20]. For example, the nonlinear VIV model by Ehsan and Scanlan [18], Larsen [19] and recently Zhu et al. [20], the 1DOF and 2DOF nonlinear flutter models [10,[16][17] and the unsteady galloping models [4,9]. These models offer the advantage of flexibility in parameter identification, as the parameters can be determined from sectional model vibration responses obtained from wind tunnel tests or computational fluid dynamics (CFD) using free or forced vibration. Consequently, they generally exhibit high accuracy and have a simple mathematical form. However, due to the frequency-dependent coefficients, these models have limitations since they only work for a single harmonic input which is a problem when considering structural nonlinearities of flexible structures [21][22].These models indicate that the aerodynamic nonlinearity of bluff body aeroelasticity is weak and can be adequately modelled using a perturbation method, reducing the modelling of aerodynamic nonlinearity to the amplitude-dependency of linear parameters [17]. This assu...

Lyapunov stability of suspension bridges in turbulent flow

“…Based on the linear assumption, past research has primarily concentrated on incipient and deterministic flutter of bridges ( [6][7][8][9][10] among others), in the wake of the pioneering works in aeronautics, where this problem has become well-known for airplane wings since the 1920s [11,12]. However, experimental observations have shown that the post-critical flutter response tends to evolve towards limit cycles, after either subcritical (see, e.g., [13,14] for a flat plate and a bridge, respectively) or supercritical bifurcations (see, e.g., [15,16] for some bridges). Furthermore, the onset of flutter instability is often significantly influenced by fluctuations in wind velocity due to turbulence, as observed by Diana [17].…”