Geometric nonlinear stiffness and frequency of the traditional spring-suspended free-vibration testing device

Abstract

Free vibration tests on bridge deck sectional models in wind tunnels have been widely adopted to study the wind-resistant performances of bridges. The traditional spring-suspended free-vibration testing device is suitable for small torsional amplitude vibration tests. When large torsional displacement occurs, a geometry nonlinear will be introduced, and the stiffness and frequency of the traditional device will change. However, quantitative research on this subject is inadequate at present. Based on proper simplifications and assumptions, new analytical formulas are derived that describe how the torsional and vertical stiffnesses of the traditional device vary as the torsional and vertical displacement change for different spring lengths, initial strains, joint spacings, and stiffnesses. The amplitude-dependent torsional frequency is also quantified based on the potential energy function. It is found that the torsional stiffness reduction rate Rα and frequency reduction rate RfAα nonlinearly increase with the torsional displacement α and amplitude Aα, respectively. In the parameter ranges considered, R10° is basically within 4%–6%, R20° is basically within 15%–28%; Rf10° is basically within 1%–2%, Rf20° is basically within 6%–11%. From the view of geometry nonlinear, the maximum torsional amplitude of the traditional device is suggested to be less than 4°. Although Rα can be effectively reduced by increasing the initial strain and length of the upper and lower springs, it cannot be completely eliminated whatever increasing the above parameters. The vertical stiffness reduction rate can be ignored.