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In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates. [ABSTRACT FROM AUTHOR]

In this paper, we consider nonlinear oscillations of a shape-morphing plate submerged in a quiescent, Newtonian, viscous fluid. We investigate the two-dimensional problem arising from two prescribed concurrent periodic motions of the plate: a rigid oscillation along its transverse direction coupled to a shape-morphing deformation to an arc of a circle with prescribed maximum curvature. As opposed to existing literature concerned with passive flexible structures, this study focuses on actively prescribed deformations of the structure as a means to manipulate the vortex-shedding and convection patterns responsible for hydrodynamic forces and power dissipation during underwater oscillations. We elucidate the potential of the proposed shape-morphing strategy in regulating the added mass and damping effects along with the hydrodynamic power dissipation both in the linear and nonlinear hydrodynamic regime, by utilizing a linear boundary integral formulation as well as computational fluid dynamics simulations. Results show the possibility of minimizing the hydrodynamic power dissipation for optimal values of the imposed curvature, along with significant reduction of the hydrodynamic forces. A simplified semianalytical argument relates these novel effects to specific geometric properties of the plate motion. Findings from this study are directly relevant to cantilever-based sensing and actuation systems operating in fluids, where control and modulation of oscillation quality factors, hydrodynamic forces, and power losses is beneficial. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of harmonic oscillations of a flanged lamina in a quiescent Newtonian incompressible viscous fluid. We conduct a comprehensive fluid–structure interaction investigation with the goal of assessing the effect of the presence of the flanges on the added mass and hydrodynamic damping experienced by the oscillating solid. We determine the complex nonlinear hydrodynamic function incorporating these effects via its real and imaginary parts, respectively, and its dependence on three nondimensional parameters that govern the flow evolution. We further investigate in detail the flow physics and the effects of nonlinearities on vortex shedding, convection, and diffusion in the vicinity of the oscillating structure. We find that the added mass effect is relatively independent of the oscillation amplitude and increases with the flange size. On the other hand, the hydrodynamic damping effect is remarkably affected by the interplay of geometry and dynamic parameters resulting into a peculiar non-monotonic behavior. We show the existence of a minimum in the hydrodynamic damping which can be attained via specific control of vortex–structure interaction dynamics and discuss its properties and significance from a physical perspective through analysis of the relevant flow fields. This novel finding has potential application for damping reduction in elastic systems where reduction of energy losses and increase of oscillation quality factor are desired. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general iterative framework to solve the dynamic problem for linear systems with non-classical viscous damping. A systematic approach is used to derive families of stationary iterative schemes that, as an instance of particular interest, decouple the equations of motion for numerical study of the system response. For such schemes, we present a detailed convergence analysis and propose several solution strategies suitable for a broad class of systems. These techniques are based on spectral analysis of particular iteration matrices arising in the derivation and aim at optimizing the convergence performance of the method. We demonstrate that the proposed systematic framework, based on a novel application of the homotopy analysis method, generalizes iterative schemes previously reported in the literature and, importantly, provides a unified perspective for the study of iterative solutions of dynamic problems. Further, we establish a connection between our results and the theory of iterative schemes for algebraic linear systems, thus providing insights on convergence results and applicability of the method. Numerical examples illustrate the effectiveness of the approach and indicate future research directions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study finite amplitude vibrations of a cantilever beam of rectangular cross section immersed in a viscous fluid under harmonic base excitation. Fluid–structure interactions are modeled through a complex hydrodynamic function that describes added mass and damping effects in response to moderately large oscillation amplitudes. The hydrodynamic function is identified from the analysis of the two-dimensional flow physics generated by a rigid rectangle undergoing harmonic oscillations in a quiescent fluid. Computational fluid dynamics is used to investigate the effects of three salient non-dimensional parameters on the flow physics and inform the formulation of a tractable expression for the hydrodynamic function. Theoretical results are validated against experimental findings on underwater vibration of compliant beams of varying cross sections. [Copyright &y& Elsevier]