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This paper numerically investigates the influence of a fixed downstream control cylinder on the flow-induced vibration of an elastically-supported primary cylinder. These two cylinders are situated in a tandem arrangement with small dimensionless centre-to-centre spacing ($L/D$, $L$ is the intermediate spacing, and $D$ is the cylinder diameter). The present two-dimensional (2D) simulations are carried out in the low Reynolds number ($Re$) regime. The primary focus of this study is to reveal the underlying flow physics behind the transition from vortex-induced vibration to galloping in the response of the primary cylinder due to the presence of another fixed downstream cylinder. Two distinct flow field regimes, namely steady flow and alternate attachment regimes, are observed for different $L/D$ and Re values. Depending on the evolution of the near-field flow structures, four different wake patterns - `2S', `2P', `2C', and `aperiodic' - are observed. The corresponding vibration response of the upstream cylinder is characterized as interference galloping and extended vortex-induced vibration. As the $L/D$ ratio increases, the lift enhancement due to flow-induced vibration is seen to be weakened. The detailed correlation between the force generation and the near-wake interactions is investigated. The present findings will augment the understanding of vibration reduction or flow-induced energy harvesting of tandem cylindrical structures.

We present a novel approach for studying the global dynamics of a vibro-impact pair, that is, a ball moving in a harmonically forced capsule. Motivated by a specific context of vibro-impact energy harvesting, we develop the method with broader non-smooth systems in mind. The seeming complications of the impacts of the ball with the capsule are exploited as useful non-smooth features in selecting appropriate return maps. This choice yields a computationally efficient framework for constructing return maps on short-time realizations from the state space of possible initial conditions rather than via long-time simulations often used to generate more traditional maps. The different dynamics in sub-regions in the state space yield a small collection of reduced polynomial approximations. Combined into a piecewise composite map, these capture transient and attracting behaviors and reproduce bifurcation sequences of the full system. Further ``separable'' reductions of the composite map provide insight into both transient and global dynamics. This composite map is valuable for cobweb analysis, which opens the door to computer-assisted global analysis and is realized via conservative auxiliary maps based on the extreme bounds of the maps in each subregion. We study the global dynamics of energetically favorable states and illustrate the potential of this approach in broader classes of dynamics., Comment: 36 pages, 27 figures

The motion of a forced vibro-impacting inclined energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top of the device. This motion occurs beyond a grazing bifurcation, at which alternating top and bottom impacts are supplemented by a zero velocity impact with the bottom of the device. For periodic forcing, we obtain semi-analytical expressions for the asymmetric periodic motion with a ratio of 2:1 for the impacts on the device bottom and top, respectively. These expressions are derived via a set of nonlinear maps between different pairs of impacts, combined with impact conditions that provide jump discontinuities in the velocity. Bifurcation diagrams for the analytical solutions are complemented by a linear stability analysis around the 2:1 asymmetric periodic solutions, and are validated numerically. For smaller incline angles, a second grazing bifurcation is numerically detected, leading to a 3:1 asymmetry. For larger incline angles, period doubling bifurcations precede this bifurcation. The converted electrical energy per impact is reduced for the asymmetric motions, and therefore less desirable under this metric., Comment: 24 pages, 9 figures, Submitted to Journal of Sound and Vibration