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Limit-cycle oscillations of bodies with airfoil cross-sections is a subject of keen interest for engineering applications. In systems consisting of multiple such closely spaced bodies, the aerodynamic interactions amongst two or more such bodies can influence the system response. The nature of these interactions is examined with respect to variations in external parameters such as freestream speed and system parameters such as inter-oscillator spacing and the number of airfoil oscillators. By using a co-simulation scheme, which consists of a reduced order three degree-of-freedom piezostructural system and an unsteady vortex lattice method fluid solver, the effects of these parameters on the resulting aerodynamic loads on the system, the overall dynamic response, and the critical flutter speed are studied. In a three-airfoil oscillator system, the effect of the position of the inner airfoil oscillator is extensively studied with a focus on characterizing airfoil interactions and airfoil-wake interactions. For different parallel configurations, studies of bifurcations with respect to different control parameters are conducted. 

With the computational resources becoming available, data-driven methods have emerged as powerful means for equation discovery and model construction. Sparse regression methods such as SINDy (Sparse Identification for Nonlinear Dynamical Systems) can be used for developing reduced-order models of nonlinear systems. In this study, the authors examine how SINDy can be used for developing low-dimensional models for airfoil systems, which experience unsteady aerodynamic loads and flutter instabilities. For a system of multiple closely spaced airfoil oscillators, analytical models are not readily available to determine flutter instabilities, and one has to take recourse to experimental and numerical means. In this work, as a starting point, data collected through simulations of unsteady aerodynamics of a single airfoil oscillator system are considered and a reduced-order model is constructed based on this data. 

Vortex-induced vibrations are oscillatory motions experienced by a body interacting with an external flow. These vibrations can be harnessed for energy harvesting purpose. A cantilever beam with a cylinder attached at the free end represents the bluff body oscillator of interest here. Vortex-induced vibrations of two adjacent bluff-body oscillators are studied by varying the transverse spacing between the oscillators. A finite element model of the system is used to numerically study the associated fluid–structure interactions. For the case with two oscillators, the effect of varying the oscillator spacing on the system response is studied. Dynamic mode decomposition is used for extracting coherent spatio-temporal structures in pressure fields. The system spectral response for the single oscillator and coupled oscillators cases are studied to examine the system dynamics. The obtained numerical results for the system dynamics are found to agree with previously reported experimental results in the literature. The present work can form a basis for constructing computational models of fluid coupled bluff-body oscillators and configuring arrays of bluff-body oscillators for energy harvesting. 

Energy harvesting from flow-induced vibrations has gained substantial attention in the last two decades due to the rising demand for renewable and sustainable energy sources, as well as the widely availability of these sources, offering a viable alternative in areas where other ambient energy sources may not be readily accessible. Flow-induced vibrations of bluff bodies are characterized by complex nonlinear dynamics, for which accurate models are currently lacking. In this work, a circular cylinder attached to the free end of a piezoelastic cantilever is considered for energy harvesting. When placed in a flow, this system undergoes vortex-induced vibrations. A reduced-order model is developed to understand fluid-structure interactions of this system. A wake oscillator has been used to describe vortex-induced vibrations and a finite-element model has been used to model the piezoelastic cantilever. The developed model is used to explore the interplay amongst the fluid, structure, and piezoelectric element. The results obtained are compared to experimental data from literature, in terms of the vibration amplitude, vibration frequency, and power obtained. Modifications to the wake oscillator model are examined to better reflect the fluid-structure interactions. It is found that there is a trade-off between accurately predicting the vibration amplitude and accurately predicting the vibration frequency. 

Abstract Freak or rogue waves are a danger to ships, offshore infrastructure, and other maritime equipment. Reliable rogue wave forecasts could mitigate this risk for operations at sea. While the occurrence of oceanic rogue waves at sea is generally acknowledged, reliable rogue wave forecasts are unavailable. In this paper, the authors seek to overcome this shortcoming by demonstrating how rogue waves can be predicted from field measurements. An extensive buoy data set consisting of billions of waves is utilized to parameterize neural networks. This network is trained to distinguish waves prior to an extreme wave from waves which are not followed by an extreme wave. With this approach, three out of four rogue waves are correctly predicted 1 min ahead of time. When the advance warning time is extended to 5 min, it is found that the ratio of accurate predictions is reduced to seven out of ten rogue waves. Another strength of the trained neural networks is their capabilities to extrapolate. This aspect is verified by obtaining forecasts for a buoy location that is not included in the networks’ training set. Furthermore, the performance of the trained neural network carries over to realistic scenarios where rogue waves are extremely rare. 

Abstract A probabilistic approach is needed to address systems with uncertainties arising in natural processes and engineering applications. For computational convenience, however, the stochastic effects are often ignored. Thus, numerical integration routines for stochastic dynamical systems are rudimentary compared to those for the deterministic case. In this work, the authors present a method to carry out stochastic simulations by using methods developed for the deterministic case. Thereby, the well-developed numerical integration routines developed for deterministic systems become available for studies of stochastic systems. The convergence of the developed method is shown and the method's performance is demonstrated through illustrative examples. 

The dynamics of mechanical systems, such as turbomachinery with multiple blades, are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and transitions between them may occur under the influence of random factors. A methodology for finding most probable escape paths and estimating the transition rates in the small noise limit is developed and applied to a collection of arrays of coupled monostable oscillators with cubic nonlinearity, small damping, and harmonic external forcing. The methodology is built upon the action plot method [Beri et al., Phys. Rev. E 72, 036131 (2005)] and relies on the large deviation theory, the optimal control theory, and the Floquet theory. The action plot method is promoted to non-autonomous high-dimensional systems, and a method for solving the arising optimization problem with a discontinuous objective function restricted to a certain manifold is proposed. The most probable escape paths between stable vibrational modes in arrays of up to five oscillators and the corresponding quasipotential barriers are computed and visualized. The dependence of the quasipotential barrier on the parameters of the system is discussed.