Nonlinearity of mechanical damping and stiffness of a spring-suspended sectional model system for wind tunnel tests

Abstract

The wind tunnel test of spring-suspended sectional models (SSSM) is an important means in the research of wind engineering, which is very frequently employed to check the performances of flutter and vortex-induced resonance of bridges as well as to identify the various aerodynamic and aeroelastic parameters of bridge components, such as aerodynamic derivatives of self-excited forces. However, in practice, the mechanical damping ratios and natural frequencies of SSSM system are prevailingly supposed to be constant in the whole procedure of a test. This assumption often leads to notable errors of the test results or dispersion of the identified aerodynamic parameters because the mechanical damping ratios and natural frequencies of SSSM system are proved to vary in fact to some extent with the change of oscillating amplitude. On that account, the mechanical nonlinearity of SSSM system is investigated and discussed in this paper by taking a flat-closed box section as a research background. The conventional linear model is firstly proved to fail to predict precisely the long-duration free decay responses of the SSSM system. The formulae of equivalent linearization approximation (ELA) are then derived by using a multiple-scale method to model the mechanical nonlinearities in the first-order approximate sense, and a time-domain system identification method is proposed on this basis to identify equivalent amplitude-dependent (EAD) damping ratio and frequency. The proposed ELA and nonlinear system identification methods are then found to be precise enough to model the mechanical nonlinearities of SSSM system. The characteristics of EAD damping ratio and frequency of both the bending and torsional modes are then discussed in detail. It is then found that the major energy dissipation of SSSM vibrations at both the bending and torsional modes generally comes from the combined effect of viscous damping and quadratic damping. However, for the vibration at the bending mode with small to moderate amplitudes, the coulomb friction damping becomes the major source of energy dissipation. Furthermore, different types of additional dampers added on the SSSM system will introduce extra mechanical nonlinearities in manners very different from each other. The liquid viscous damper with oil tank form employed in this study is found to be an ideal linear damper, whereas the steel wire-rope-circle damper of friction type brings in significant mechanical nonlinearities.