Added Mass Ratio Research Articles

Effects of mass and damping ratios on the flow-induced vibration of two staggered circular cylinders

The mass ratio between structure and fluid and the structural damping ratio have been shown to significantly affect the flow-induced vibration (FIV) of an isolated circular cylinder. Their influences on multiple staggered circular cylinders commonly found in offshore structures have, however, not been clearly understood. This study numerically investigates the vibration responses and flow field of two staggered circular cylinders with the shear stress transfer k–ω turbulence model and the overset mesh method. The accuracy of the numerical method adopted is validated against published experimental results, and the effects of the mass ratio and damping ratio on FIV are systematically investigated. The structural responses of the two cylinders are found more sensitive to the mass ratio than the damping ratio. The amplitude of vibration increases, in general, with a reduction in the mass ratio or damping ratio, and the vibration is much more significant when the mass ratio is less or equal to unity as compared to those from other mass ratio values. A reduction in the mass ratio is found leading to more diverse vortex shedding modes with fast transition from one into another. The self-excited dynamic forces represented by the added mass ratio ma* and added damping ratio ζa are further analyzed. It is found that the added mass ratio is positive under low inflow velocity, and it gradually becomes negative with higher inflow velocity. The added damping ratio is generally negative under low inflow velocity and it increases with the inflow velocity. Furthermore, the added damping ratio decreases with the inflow velocity only when the mass ratio is smaller than unity.

Intrinsic features of flow-induced stability of a square cylinder

Vortex-induced vibrations and galloping of an elastically mounted square cylinder are investigated for cylinder mass ratio m* = 2–50, damping ratio ζ = 0–1.0, mass-damping ratio m*ζ = 0–50 and flow reduced velocity Ur = 1–80. We home in on the effects of m*, ζ, m*ζ, $({m^\ast } + m_{a\textrm{0}}^\ast )\zeta$ and $({m^\ast } + m_{ae}^\ast )\zeta$ on the critical reduced velocity Urc marking the onset of galloping, where $m_{a\textrm{0}}^\ast $ is the quiescent-fluid added mass ratio and $m_{ae}^\ast $ is the effective added mass ratio. Vibration responses, forces, vibration frequencies and added mass ratios are studied and discussed. The different branches of vortex-induced vibrations have different dependencies of $m_{ae}^\ast $ on Ur. The $m_{ae}^\ast $ in the initial branch is positive and drops rapidly with Ur, but that in the lower branch is negative and declines gently. In the galloping regime, $m_{ae}^\ast $ jumps from negative to positive at the onset of galloping, declining slightly with increasing Ur. Our results and prediction equations show that when ζ = 0, Urc is independent of m* for m* ≥ 5, albeit slightly higher for m* = 3. The latter is ascribed to mode competition. When ζ > 0, Urc linearly increases with increasing ζ. Detailed analysis substantiates that m*ζ or $({m^\ast } + m_{a\textrm{0}}^\ast )\zeta$ does not serve as the unique criterion to predict the galloping occurrence. Here, we propose a new combined mass-damping parameter $({m^\ast } + m_{ae}^\ast )\zeta$ in the relationship between galloping onsets and structural properties, which successfully scales all data of Urc at different m* and ζ values.

Effectively reduce transient vibration of 2D wing with bi-stable metamaterial

Unsteady time-varying flow during flight may causes transient vibrations of wings, limiting aircraft safety and requiring effective suppression methods. Nonlinear acoustic metamaterials have recently attracted extensive attention owing to their superior capability for low-frequency and broadband vibration suppression. However, most existing nonlinear metamaterials consist of mono-stable nonlinear resonators, whose transient vibration reduction capability requires significant improvement. This paper proposes a 2D metamaterial wing model consisting of bi-stable nonlinear resonators. Based on CFD simulation, we establish an equivalent model surrounded by a fluid-like medium and systematically investigate its transient dynamics and energy dissipation. Results indicate that the bi-stable metamaterial can quickly dissipate the transient vibrations of the wing with an efficiency much higher than the linear and mono-stable nonlinear counterparts. An energy dissipation rate of over 75 % is achievable with an added mass ratio of 4 %–8 %, while the energy dissipation rate of the linear counterpart is below 60 %. The subharmonic nonlinear beatings and subharmonic resonance capture, such as 1:2 or 2:3 resonances between multiple modes, are essential mechanisms for the improvement. The reduction is robust to varying amplitudes and the distance between the two stable states. These findings provide new ways to reduce the fluid-structure interaction transient vibrations of structures.

Double-order coupling bandgap design of metamaterial beams and broadband vibration reduction properties

<sec>Local-resonance bandgap and Bragg bandgap can coexist in a metamaterial beam, and their coupling effect can be used to realize ultra-wide bandgap, which has great potential applications in the field of wide-band vibration reduction. Previous studies usually considered the single-order coupling between the local-resonance bandgap and Bragg bandgap in metamaterial beams with a single array of local resonators, which can only achieve the single-order ultra-wide coupling bandgap and cannot meet the wide-band vibration reduction requirements of double/multiple target frequency bands. In this paper, metamaterial beams with double arrays of local resonators are considered, and the regulation design and analysis of double-order coupling of local-resonance and Bragg bandgaps are carried out based on an analytical model of bending wave dispersion relation. Moreover, the vibration reduction characteristics of the double-frequency-resonator metamaterial beams with double-order coupling bandgaps are studied by using spectral element method and the finite element method. The main conclusions are as follows.</sec><sec>1) A design method is proposed for realizing double-order coupling wide bandgap in a metamaterial beam with double arrays of local resonators. By using this method, the resonance frequencies of the local resonators can be quickly designed on conditions that host beam parameters, lattice constant and added mass ratio of the local resonators are given.</sec><sec>2) The double-order coupling bandgaps in a metamaterial beam carrying double arrays of local resonators are compared with the single-order coupling bandgaps in metamaterial beams with a single array of local resonators. It is found that through proper design, the total normalized width of the double-order coupling bandgap can be much broader than that of the single-order coupling bandgap, so the double-order coupling bandgap is more beneficial to wide-band vibration reduction.</sec><sec>3) It is found that for a given total added mass ratio of the double arrays of local resonators, it is necessary to optimize the mass distribution ratio of the double resonators to maximize the total normalized width of double-order coupling bandgap. An approximate formula for designing the optimal mass distribution ratio of the double resonators is further established.</sec><sec>4) The spectral element method is used to study the vibration reduction characteristics of the metamaterial beams carrying double arrays of local resonators designed based on double-order bandgap coupling. The accuracy of the spectral element method is verified by comparing with the finite element method. The results show that significant vibration reduction can be achieved in two wide frequency bands corresponding to the double-order coupling bandgaps. The influences of number of unit cells and resonator damping on the vibration reduction characteristics of the metamaterial beam are further analyzed. It is shown that the increase of number of unit cells can enhance the vibration reduction performance in the bandgap, and the increase of resonator damping can effectively broaden the vibration reduction frequency band.</sec>

EXAFS investigation of strontium adsorption onto weathered biotite

The efficiency of the sorption of Sr2+ on weathered biotite (WB), a type of clay mineral, was investigated. Removal of Sr2+ and Cs+ is important in the treatment of contaminated water from the 1F accident, which is one of the radionuclide waste treatment problems. We focused on developing an adsorption method for Sr ions using WB, which is abundant in Fukushima. Applying a molten salt treatment, the amount of sorbed Sr2+ simply increased as the added mass ratio of strontium chloride (SrCl2) increased from 1:1, 1:5, and 1:10 for the onefold, fivefold, and tenfold additions of SrCl2, respectively. Then, the crystal structure of WB as an adsorbent was evaluated by x-ray diffraction (XRD) analysis. Thus, it was observed that the WB retained its original crystal structure even after the sorption of Sr2+. Extended x-ray absorption fine structure (EXAFS) analysis was performed to investigate the local sorption structure of Sr2+ in the WB. The results revealed that Sr2+ was preferentially sorbed into the SiO4 and Al2O3 layers when Sr2+ was in the low mass ratio, whereas it was mainly sorbed into the SiO4 layer when the ratio was high.

An analytical approach for modelling the vibroacoustic behaviour of a heavy fluid-loaded plate near a free surface

Predictions of the vibroacoustic response of a point-force excited baffled thin rectangular plate immersed in a heavy fluid and near a free surface are presented using an analytical model. The equations of motion are solved by Fourier analysis, where the eigenfunctions of plate vibration form the basis of spatial expansion for fluid loading. Vibroacoustic indicators, including the plate velocity, acoustic pressure, and acoustic power, are predicted using the analytical approach and verification is performed by comparison with finite element simulations. The results have shown that variations in the height of the free surface can have a significant effect on these indicators. From the vibration response, added mass effect due to heavy fluid loading is altered and further investigated with the explicit evaluation of an added mass ratio for different free surface heights for the first five plate modes. For a given height of a free surface, standing waves can form between the free surface and baffled plate at specific excitation frequencies and slightly alters the acoustic pressure spectra. This condition also presents an effect on the acoustic power, where the first standing wave frequency dictates the efficient sound radiation to the far field.

Application of the in-situ biological detoxification polymer for the improvement of AFB1 detoxification

A novel biological detoxification polymer (BDP) was in-situ synthesis by the co-immobilization of the compound enzymes (laccase and Aspergillus niger crude enzyme) and the aminated mesoporous silica nanoparticles (MSN-NH2) with zeolitic imidazolate framework-8 (ZIF-8) for the detoxification of aflatoxin B1 (AFB1). The ZIF-8 shell of BDP acted as the AFB1 adsorbent around the compound enzymes inside the BDP. The detoxification rate of BDP at 35 °C for 24 h was 96.7%. The detoxification of AFB1 with the added mass ratio of BDP 1% to moldy corn was 65.8%. After the BDP was stored at 4 °C for 30 d, the enzyme activity remained 70.9%. Moreover, the enzyme activity and detoxification rate with BDP remained 80.7% and 80.0%, respectively, after the fourth repeated detoxification. The compound enzymes acted on the C–O bond and methoxyl group in the side chain of AFB1. Three degradation products (C16H16O5, C16H14O4, C15H14O2) with different structures were detected in the degradation of AFB1 with the BDP. Application of the in-situ BDP represents a promising way to improve the detoxification of AFB1.

Scaling the dynamic response and stability of composite hydrodynamic lifting surfaces

Imperfectly scaled models are commonplace in aerodynamics and hydrodynamics because few facilities can meet all the flow and structural scaling requirements. The objectives of this work are to (1) derive and numerically validate scaling relations for the steady-state and dynamic hydroelastic response and stability of hydrodynamic composite lifting surfaces and (2) to investigate the effect of imperfect scaling on the steady-state and dynamic response, as well as hydroelastic stability of said surfaces. We derive proper scaling laws and validate them through numerical simulations using unsteady potential flow and composite beam theory. We investigate the prediction of inception of a new, low-frequency mode that only develops at sufficiently high speeds using scaled models. We demonstrate scaling effects on the modal frequencies, damping coefficients, and hydroelastic instability boundaries by comparing cases with fully enforced scaling laws and cases with relaxed similarities. Using the same material for both the prototype and reduced length-scale models results in imperfect scaling; the steady-state and dynamic hydroelastic responses are not scaled, and smaller length-scale models exhibit delayed hydroelastic instabilities. The conclusion is that using appropriate materials for model scale tests to satisfy Cauchy number similarity is necessary for similar steady-state response, but dynamic similarity additionally requires similar solid-to-fluid added mass ratio. Proper scaling allows one to accurately interpret and assess the performance and stability of full-scale flexible composite lifting surfaces such as foils, propulsors, turbines, fins, rudders, energy saving devices, and energy harvesters.

Radiation-induced instability of a finite-chord Nemtsov membrane

We consider a problem of stability of a membrane of an infinite span and a finite chord length, submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov [“Flutter effect and emission in the region of anomalous and normal Doppler effects,” Radiophys. Quantum Electron. 28(12), 1076–1079 (1985)] has shown that an infinite-chord membrane is susceptible to flutter instability due to the excitation of long gravity waves on the free surface if the velocity of the flow exceeds the phase velocity of the waves and related this phenomenon with the anomalous Doppler effect. In the present work, we derive a full nonlinear eigenvalue problem for an integrodifferential equation for the finite-chord Nemtsov membrane in the finite-depth flow. In the shallow- and deep-water limits, we develop a perturbation theory in the small added mass ratio parameter acting as an effective dissipation to find explicit analytical expressions for the frequencies and the growth rates of the membrane modes coupled to the surface waves. We find an intricate pattern of instability pockets in the parameter space and describe it analytically. The case of an arbitrary depth flow with free surface requires numerical solution of a new non-polynomial nonlinear eigenvalue problem. We propose an original approach combining methods of complex analysis and residue calculus, Galerkin discretization, Newton method, and parallelization techniques implemented in MATLAB to produce high-accuracy stability diagrams within an unprecedented wide range of a system's parameters. We believe that the Nemtsov membrane plays the same paradigmatic role for understanding radiation-induced instabilities as the Lamb oscillator coupled to a string has played for understanding radiation damping.

Transition to chaos in the flow-induced vibration of a pitching–plunging airfoil at low Reynolds numbers: Ruelle–Takens–Newhouse scenario

This study focuses on numerically analyzing the transition from periodic to chaotic dynamics in the fluid-elastic response of a 2-dof flexibly-mounted airfoil with chord-wise rigidity. The computational framework is composed of a high fidelity Navier–Stokes solver, weakly coupled with a structural model having geometric nonlinearity represented by cubic order stiffness terms. A low Reynolds number flow regime and a very low structure-to-fluid added mass ratio have been considered to simulate the flying conditions of very light-weight unmanned devices. A bifurcation analysis of the system, in the absence of actuation or control forces, is undertaken with the wind velocity as the control parameter. The route to chaos – identified to be the Ruelle–Takens–Newhouse quasi-periodic route – is established for the first time for a flexible pitch–plunge flapping system. Robust nonlinear time series analysis techniques have been implemented to characterize different complex dynamical states present in the system.

Merging mechanical and electromechanical bandgaps in locally resonant metamaterials and metastructures

Locally resonant metamaterials are characterized by bandgaps at wavelengths much larger than the lattice size. Such locally resonant bandgaps can be formed using mechanical or electromechanical resonators. However, the nature of bandgap formation in mechanical and electromechanical (particularly piezoelectric) metamaterials is fundamentally different since the former is associated with a dynamic modal mass, while the latter is due to a dynamic modal stiffness. Next-generation metamaterials and resulting metastructures (i.e. finite configurations with specified boundary conditions) hosting mechanical resonators as well as piezoelectric interfaces connected to resonating circuits can enable the formation of two bandgaps, right above and below the design frequency of the mechanical and electrical resonators, respectively, yielding a wider bandgap and enhanced design flexibility as compared to using a purely mechanical, or a purely electromechanical configuration. In this work, we establish a fully coupled framework for hybrid mechanical-electromechanical metamaterials and finite metastructures. Combined bandgap size is approximated in closed form as a function of the added mass ratio of the resonators and the system-level electromechanical coupling for the infinite resonators approximation. Case studies are presented for a hybrid metamaterial cantilever under bending vibration to understand the interaction of these two locally resonant metamaterial domains in bandgap formation. Specifically, it is shown that the mechanical and electromechanical bandgaps do not fully merge for a finite number of resonators in an undamped setting. However, the presence of even light damping in the resonators suppresses the intermediate resonances emerging within the combined bandgap, enabling seamless merging of the two bandgaps in real-world structures that have damping. The overall concept of combining mechanical and electromechanical bandgaps in the same single metastructure can be leveraged in more complex topologies of piezoelectric metamaterial-based solids and structures.

A general theory for bandgap estimation in locally resonant metastructures

Locally resonant metamaterials are characterized by bandgaps at wavelengths that are much larger than the lattice size, enabling low-frequency vibration attenuation. Typically, bandgap analyses and predictions rely on the assumption of traveling waves in an infinite medium, and do not take advantage of modal representations typically used for the analysis of the dynamic behavior of finite structures. Recently, we developed a method for understanding the locally resonant bandgap in uniform finite metamaterial beams using modal analysis. Here we extend that framework to general locally resonant 1D and 2D metastructures (i.e. locally resonant metamaterial-based finite structures) with specified boundary conditions using a general operator formulation. Using this approach, along with the assumption of an infinite number of resonators tuned to the same frequency, the frequency range of the locally resonant bandgap is easily derived in closed form. Furthermore, the bandgap expression is shown to be the same regardless of the type of vibration problem under consideration, depending only on the added mass ratio and target frequency. For practical designs with a finite number of resonators, it is shown that the number of resonators required for the bandgap to appear increases with increased target frequency, i.e. more resonators are required for higher vibration modes. Additionally, it is observed that there is an optimal, finite number of resonators which gives a bandgap that is wider than the infinite-resonator bandgap, and that the optimal number of resonators increases with target frequency and added mass ratio. As the number of resonators becomes sufficiently large, the bandgap converges to the derived infinite-resonator bandgap. Furthermore, the derived bandgap edge frequencies are shown to agree with results from dispersion analysis using the plane wave expansion method. The model is validated experimentally for a locally resonant cantilever beam under base excitation. Numerical and experimental investigations are performed regarding the effects of mass ratio, non-uniform spacing of resonators, and parameter variations among the resonators.

Influence of flow-induced bend–twist coupling on the natural vibration responses of flexible hydrofoils

For flexible hydrofoils, the natural flow-induced bending and twisting deformations are coupled if the center of lift is away from the elastic axis; this coupling may be influenced by viscous effects due to movement in the center of lift. The objective of this work is to investigate the role of flow-induced bend–twist coupling effects, as well as their dependence on the reduced velocity and solid-to-fluid added mass ratio. A secondary objective is to compare inviscid and viscous fluid–structure interaction (FSI) simulations of the natural flow-induced vibration responses of flexible cantilevered hydrofoils in water. The focus is on attached flow conditions in fully turbulent regimes at low angles of attack, where inviscid FSI method should be relatively accurate, and the foil response should be dominated by the foil's natural frequencies. The viscous FSI model is formulated by coupling a two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) model with a two-degrees-of-freedom (2-DOF) model representing the spanwise tip bending and twisting deformations. The results show that the flow-induced bend–twist coupling terms are important for accurate prediction of the natural vibration frequencies and damping characteristics, particularly for the twisting motion, and their relative importance grows when the relative velocity increases and the solid-to-fluid added mass ratio decreases.

Numerical and experimental investigation of natural flow-induced vibrations of flexible hydrofoils

The objective of this work is to present combined numerical and experimental studies of natural flow-induced vibrations of flexible hydrofoils. The focus is on identifying the dependence of the foil’s vibration frequencies and damping characteristics on the inflow velocity, angle of attack, and solid-to-fluid added mass ratio. Experimental results are shown for a cantilevered polyacetate (POM) hydrofoil tested in the cavitation tunnel at the French Naval Academy Research Institute (IRENav). The foil is observed to primarily behave as a chordwise rigid body and undergoes spanwise bending and twisting deformations, and the flow is observed to be effectively two-dimensional (2D) because of the strong lift retention at the free tip caused by a small gap with a thickness less than the wall boundary layer. Hence, the viscous fluid-structure interaction (FSI) model is formulated by coupling a 2D unsteady Reynolds-averaged Navier-Stokes (URANS) model with a two degree-of-freedom (2-DOF) model representing the spanwise tip bending and twisting deformations. Good agreements were observed between viscous FSI predictions and experimental measurements of natural flow-induced vibrations in fully turbulent and attached flow conditions. The foil vibrations were found to be dominated by the natural frequencies in absence of large scale vortex shedding due to flow separation. The natural frequencies and fluid damping coefficients were found to vary with velocity, angle of attack, and solid-to-fluid added mass ratio. In addition, the numerical results showed that the in-water to in-air natural frequency ratios decreased rapidly, and the fluid damping coefficients increased rapidly, as the solid-to-fluid added mass ratio decreases. Uncoupled mode (UM) linear potential theory was found to significantly over-predict the fluid damping for cases of lightweight flexible hydrofoils, and this over-prediction increased with higher velocity and lower solid-to-fluid added mass ratio.

Dynamical Stability Analysis of a Fluid Structure Interaction System Using a High Fidelity Navier-stokes Solver

The present paper investigates the flow induced dynamics of a non-linear fluid-structure interaction (FSI) system comprising of a symmetrical NACA 0012 airfoil supported by non-linear springs. Two methods are used in calculating the aerodynamic loads: a linear analytical approach and a full Navier-Stokes (N-S) solution. The analytical approach is based on the assumption of potential flow theory and a rigid wake. Wind velocity as a bifurcation parameter shows that the structural response undergoes a supercritical Hopf bifurcation. However, the analytical loads predict unrealistic bifurcation onset at low values of solid to fluid added mass ratio (μ) relevant to the application of flapping wing micro air vehicles (MAVs), showing the extremely large amplitude of oscillations. These observations render the use of an inviscid approach meaningless at such parametric regimes. Hence, we propose to use a N-S solver to emphasize the limit of applicability of the linear aerodynamic theory. Moreover, the inclusion of the viscous effects can potentially result in interesting dynamical behavior that has not been captured by the analytical approach. A bifurcation and stability analysis has been carried out for different parametric variations of μ in the fluid structure interaction system.

Dynamic response and stability of a flapping foil in a dense and viscous fluid

It is important to understand and accurately predict the static and dynamic response and stability of flexible hydro/aero lifting bodies to ensure their structural safety, to facilitate the design/optimization of new/existing concepts, and to test the feasibility of using advanced materials. The present study investigates the influence of solid-to-fluid added mass ratio (\documentclass[12pt]{minimal}\begin{document}$\sqrt{\mu _b}$\end{document}μb) and viscous effects on the fluid-structure interaction (FSI) response and stability of a flapping foil in incompressible and turbulent flows using a recently presented efficient and stable numerical algorithm in time-domain, which couples an unsteady Reynolds Average Navier-Stokes solver with a two degrees-of freedom structural model. The new numerical coupling method is able to stably and accurately simulate the FSI behavior of light foils in dense fluids: a limit which is known to be numerically difficult to study with classical FSI coupling methods. The studied FSI responses include static/dynamic divergence and flutter instabilities, which are compared with inviscid, linear potential theory predictions obtained with both time and frequency domain formulations, as well as with several published experimental data. In general, the results show that the critical reduced flutter velocities and reduced divergence velocities both decrease as \documentclass[12pt]{minimal}\begin{document}$\sqrt{\mu _b}$\end{document}μb decreases, and are captured with good accuracy using the viscous FSI solver for a wide range of relative mass ratios that are typical to air/hydrofoils. The comparative analyses showed that the classic frequency-domain linear potential theory is severely unconservative for predicting the flutter velocity for cases with \documentclass[12pt]{minimal}\begin{document}$\sqrt{\mu _b}<3$\end{document}μb<3: this includes the typical operating conditions of most marine and biomedical lifting devices, where the fluid forces are comparable to the solid forces, and strong nonlinear interactions may develop. In addition, the viscous FSI solver is shown to correctly predict the experimentally reported critical divergence speed of a light foil in a dense fluid for a case where the classical potential theory predicts an infinite divergence speed as the foil's elastic axis (E.A.) coincided with the aerodynamic center. The results show that static/dynamic divergence will occur before flutter for light hydrofoils with an E.A. downstream of the center of pressure. However, for high solid-to-fluid added mass ratios (\documentclass[12pt]{minimal}\begin{document}$\sqrt{\mu _b}>2$\end{document}μb>2), flutter tends to occur prior to divergence. In addition, in between the regions governed by static divergence (\documentclass[12pt]{minimal}\begin{document}$\sqrt{\mu _b}<1$\end{document}μb<1) and flutter (\documentclass[12pt]{minimal}\begin{document}$\sqrt{\mu _b}>2$\end{document}μb>2), there is a dynamic divergence region, where the foil deformations oscillate with an increasing mean amplitude, and the oscillation frequency decreases toward zero as the deformation increases; this region could only be captured by using a viscous FSI solver.

A SIMPLE DESIGN METHOD FOR TUNED DYNAMIC MASS SYSTEMS

This paper introduces a simple design method for tuned dynamic mass(D.M.) systems with very large added mass ratio which is the value of D.M.(rotating inertial mass) to mass of the main structure. The method is constructed on the bases of rule of geometric mean and rule of difference/sum for the natural periods computed under the particular conditions of viscous damping factors of hd= 0 and hd= ∞. The rules are derived from the properties of the invariant point theory. The paper shows that the structures can be designed by the proposed method, which hold viscous damping factors more than 0.2 for the 1st and 2nd modes.