An experimental investigation on the dual-resonance revealed in the VIV of flexible cantilevers with orthotropic bending stiffness

Abstract

This article presents an experimental investigation on the dynamic behavior of orthotropically stiffened cantilevered flexible cylinders, mounted in vertical configuration, undergoing vortex-induced vibrations (VIV). The investigation was motivated by intriguing results published in 2001, regarding a flexible cylinder with orthotropic bending stiffness, presenting the first natural frequencies ratio parameter f1*=f1x/f1y=4.08 (x and y are the in-line and crosswise directions, respectively), in which a new high amplitude-frequency response branch was revealed in the range U*>12 (amplitudes measured at the free tip), then named “High Speed Mode Branch” (HSMB). The present investigation goes further, by studying the influence of the first natural frequency ratio parameter f1* on VIV. Four cantilevered flexible cylinders were tested, each one presenting a distinct nominal frequencies ratio, namely f1*=1:1, 2:1, 3:1 and 4:1. The experiments were carried out in a recirculating water-channel with the stream flow varied continuously, by slowly increasing the velocity, instead of doing it by steps. An innovative data analysis methodology was developed to deal with the resulting slowly nonstationary signals by combining the Galerkin's projection scheme with the Hilbert-Huang Transform technique. The influence of the first natural frequency ratio parameter is shown as determining the position and width of the reduced velocity range in which dual resonance occurs. Moreover, f1*>1.0 allows higher reduced velocities to be reached, therefore, enabling the appearance of higher modes of crosswise vibration. The HSMB appearance is now recognized as a result of the combination of the first crosswise mode response and the onset of amplitudes related to the second crosswise mode of vibration. The results here presented may serve as a new benchmark data for modeling and simulations involving VIV of flexible cylinders equipped with orthotropic bending stiffness.