Griffin plots of vortex-induced vibrations: revealing self-similarity for estimation from transient displacement responses

Abstract

Griffin plot relates the peak amplitudes of vortex-induced vibration to structural mass-damping parameter, known as the Scruton number. Griffin plot serves as a fundamental tool in many engineering fields. This study confirms a general self-similarity in Griffin plots, where plots derived from transient responses at any Scruton number converge to a single, consistent curve. This self-similarity arises from weak aeroelastic nonlinearity in vortex-induced vibration, manifesting as amplitude-dependent aerodynamic damping. Based on this self-similarity behavior, we propose a numerical method to estimate Griffin plots from transient displacement responses at any Scruton number. The resulting plots align closely with experimental data for both cross-flow and torsional vortex-induced vibrations, highlighting robust self-similar behavior across different Scruton numbers. Furthermore, for a rectangular cylinder, closed-box deck, and double-girder deck, we observe a consistent trend in the Griffin plots: the reciprocal of the peak VIV amplitudes exhibits an approximately linear dependence on the Scruton number, particularly for torsional oscillations. Motivated by this observation, we formulate a simple empirical model for the vortex-induced forces. Using aeroelastic parameters identified from only a single Scruton number, the model successfully reproduces the entire Griffin plot for a rectangular cylinder, thereby greatly reducing the need for extensive experimental data.