FIV 2018-167 AN EXPERIMENTAL INVESTIGATION ON VORTEX-INDUCED VIBRATIONS OF CANTILEVERED FLEXIBLE CYLINDERS WITH ORTHOTROPIC BENDING STIFFNESS

This paper presents further experimental investigations on vortex-induced vibrations (VIV) of cantilevered flexible cylinders with orthotropic bending stiffness. Four cantilevered flexible cylinders with distinct orthotropic bending ratios were built, by molding thin aluminum stiffeners, of rectangular cross section, inside the cylinders made of a flexible resin. The natural frequency ratio corresponding to in-line and crosswise vibration modes, f = f1x f1y ⁄ , was set to 4, 3, 2 and 1. A series of experimental runs was carried out, under ascending and descending flow speeds. The existence of a stable ‘high speed branch response’ in the cross wise direction, firstly revealed in 2001 by Fujarra et al [1] has been confirmed. This paper aims at presenting some results and discussing the effect of the bending stiffness ratio on this peculiar vibration response branch and how it regulates dual resonance regimes. INTRODUCTION Two degrees of freedom VIV (2DoF VIV) of rigid cylinders mounted on linear elastic supports have been focus of analysis for decades; [2] [4] . The effect of in-line oscillation on crosswise vibrations has been vastly studied for low mass-damping cylinders; see, e.g., [5] . Motivated by ocean engineering problems regarding cables and risers, even low aspect ratio or yawed cylinders have attracted attention; [6] [7] . Moreover, VIV of flexible cylinders have also been the subject of many recent investigations; see, [8] [10] . Particularly, experiments on cantilevered flexible cylinders have been studied for more than two decades; [3] A pioneer experimental work with a cantilevered flexible cylinder, [11] , showed the existence of a short and high-amplitude response branch in the first crosswise mode, extending in the range 8.3 < U = U f1yD ⁄ < 10, just to the right of a branch that was later identified as a super-upper response branch, [12] , within a comparison with experiments by Jauvtis and Williamson, [5] , with 2DoF rigid cylinders. Such a short and high-amplitude response branch was visually observed as triggered by structural perturbation, characterizing for a strong coupling between in-line and cross-wise vibrating modes. At that time, just cross wise vibrations were accessed through straingage measurements and mode decomposition techniques. A few years later the pioneer finding [11] , the same kind of ‘high speed mode branch’ in cantilevered flexible cylinders subjected to VIV was revealed by Fujarra et al. [1] . That work studied a flexible cylinder with orthotropic bending stiffness in a recirculating water channel, by setting the ratio between the first natural frequencies, in the in-line and cross-wise directions to the flow, f = f1x f1y ⁄ , very close to four (4.08). Such a stable response branch, triggered by either, structural or upstream hydrodynamic perturbations, was characterized by cross-wise amplitudes of order of one diameter coupled to relatively large in-line vibrations and by high frequencies components in the energy spectrum, so that it might be also called a “high energy response branch”. In that experiment, the ‘high speed mode branch’ extended in the reduced velocity interval 12 < U = U f1yD ⁄ < 20, appearing to be extinguished by the onset of the second transverse vibration mode lock-in. Meanwhile, the VIV scientific community, driven by the same ocean engineering motivations, restarted to investigate the effect of the natural frequency ratio in rigid cylinders responses that had been pioneered by Sarpkaya, [13] , in 1995. In fact, a thorough investigation on such effects have been carried out by several research groups, from 2006 on, particularly concerned on dual resonance regimes; see, e.g., [14] [19] . Cross-wise amplitude responses at higher reduced velocities have been observed,