Showing papers on "Added mass published in 2013"

Nonlocal mass nanosensors based on vibrating monolayer graphene sheets

Abstract: Single layer graphene sheets (SLGS) as a nanoscale label-free mass sensor are proposed. A mathematical framework according to nonlocal elasticity is considered. The nonlocal elasticity incorporates the small-scale effects or nonlocality in the analysis. Rectangular graphene resonators are assumed to be in cantilevered configuration. Closed-form nonlocal equations are derived for the frequency shift due to the added mass based on four types of different mass loadings. From the potential and kinetic energy of the mass loaded graphene sheets, generalised nondimensional calibration constants are proposed for an explicit relationship among the added mass, nonlocal parameter and the frequency shift. These equations based on nonlocal elasticity in turn are used for sensing the added mass (e.g. adenosine bio-fragment). Molecular mechanics simulation is used to validate the new nonlocal sensor equations. The optimal values of span of nonlocal parameter are used and compared with the molecular mechanics simulation results. The nonlocal approach generally predicts the frequency shift accurately compared to the local approach in most cases. Numerical results show the importance of considering the distributed nature of the added mass while using the nonlocal theory. The performance of the sensor is governed on the spatial distribution of the attached mass on the graphene sheet. Discussion on the numerical results illustrate that the sensitivity of graphene sensors is in the order of Gigahertz/zeptogram.

Coupled vibration of a cantilever micro-beam submerged in a bounded incompressible fluid domain

Abstract: This paper investigates the free vibrations of a cantilever micro-beam submerged in a bounded frictionless and incompressible fluid cavity. Based on the Fourier–Bessel series expansion and using linear potential theory, an analytical method is proposed to analyze the eigenvalue problem, where the fluid effect emerges as an added mass. Wet beam vibration mode shapes together with the sloshing modes of the oscillating liquid are depicted. Moreover, effects of geometrical configuration and fluid density on the natural frequencies of the coupled system are evaluated. Results show that in spite of the high added mass values related to lower modes, presence of the fluid changes the higher modes more effectively.

Energy harvesting from underwater torsional vibrations of a patterned ionic polymer metal composite

Abstract: In this paper, we study underwater energy harvesting from torsional vibrations of an ionic polymer metal composite (IPMC) with patterned electrodes. We focus on harmonic base excitation of a centimeter-size IPMC, which is modeled as a slender beam with thin cross-section vibrating in a viscous fluid. Large-amplitude torsional vibrations are described using a complex hydrodynamic function, which accounts for added mass and nonlinear hydrodynamic damping from the surrounding fluid. A linear black box model is utilized to predict the IPMC electrical response as a function of the total twist angle. Model parameters are identified from in-air transient response, underwater steady-state vibrations, and electrical discharge experiments. The resulting electromechanical model allows for predicting energy harvesting from the IPMC as a function of the shunting resistance and the frequency and amplitude of the base excitation. Model results are validated against experimental findings that demonstrate power harvesting densities on the order of picowatts per millimeter cubed.

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

Abstract: 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 (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 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 μb 2), flutter tends to occur prior to divergence In addition, in between the regions governed by static divergence (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

Hydrodynamic forces induced by transient sloshing in a 3D rectangular tank due to oblique horizontal excitation

Abstract: A time-independent finite difference method is developed to simulate fluid sloshing in a three-dimensional tank. The developed numerical scheme is verified by the rigorous benchmark tests. The experiment measurement of liquid sloshing in a 3D tank was also carried out in this study to further validate the accuracy of the present numerical results. Transient waves can change their types naturally in the time domain, especially for a tank excited by resonant frequencies. In this study, if the excitation frequencies are far from the fundamental natural frequency and there are four types of stable sloshing waves discovered due to the oblique horizontal excitation: “diagonal”, “single-directional”, “square-like”, and “irregular” waves. Besides, the swirling waves can only be generated for a partially-filled tank excited at near resonant frequency with oblique horizontal excitation. The evolution of forces induced by different sloshing waves acting on the tank walls is calculated and discussed in this work. In addition, the dynamics of sloshing force induced by swirling waves are explored in detail. The force of the single-directional waves acting on the tank bottom is time-invariant but the other types of sloshing waves show a beating phenomenon which is attributed to the momentum flux across the free surface and the vertical inertia of sloshing fluid. The effect of various oblique excitation directions of the tank on liquid sloshing is discussed as well. The horizontal hydrodynamic force of sloshing waves acting on the mid-section of the left wall of the tank is dominated by the added mass effect if the external excitation frequency is larger than 4 times the lowest natural frequency ( ω 1 ) of the tank with partially-filled fluid. On the other hand, the wave elevation of sloshing waves plays a key effect on the horizontal sloshing-induced force when the excitation frequency of the tank is less than 4 ω 1 . A novel mechanism is presented to describe the phenomenon of alternate switch directions of the swirling waves. The relationship between the external force and the sloshing hydrodynamic force is the major factor to trigger the switch direction of the swirling waves. The influence of different base ratios of a rectangular tank on kinematic and dynamic responses of sloshing fluid is also explored in this work.

Volume displacement effects during bubble entrainment in a travelling vortex ring

Abstract: When a few bubbles are entrained in a travelling vortex ring, it has been shown that, even at extremely low volume loadings, their presence can significantly affect the structure of the vortex core (Sridhar & Katz, J. Fluid Mech., vol. 397, 1999, pp. 171–202). A typical Euler–Lagrange point-particle model with two-way coupling for this dilute system, wherein the bubbles are assumed subgrid and momentum point sources are used to model their effect on the flow, is shown to be unable to capture accurately the experimental trends of bubble settling location, bubble escape and vortex distortion for a range of bubble parameters and vortex strengths. The bubbles experience significant amounts of drag, lift, added mass, pressure and gravity forces. However, these forces are in balance with each other as the bubbles reach a mean settling location away from the vortex core. The reaction force on the fluid due to the net summation of these forces alone is thus very small and is unable to affect the vortex core. By accounting for fluid volume displacement due to bubble motion, experimental trends on vortex distortion and bubble settling location are captured accurately. The fluid displacement effects are studied by computing various contributions to an effective volume displacement force and are found to be important even at low volume loadings. As the bubble size and hence bubble Reynolds number increase, the bubbles settle further away from the vortex centre and have strong potential for vortex distortion. The net volume displacement force depends on the radial pressure force, the radial settling location of the bubble, as well as the vortex Reynolds number. The resultant of the volume displacement force is found to be roughly at with the vortex travel direction, resulting in wakes directed towards the vortex centre. Finally, a simple modification to the standard point-particle two-way coupling approach is developed wherein the interphase reaction source terms are consistently altered to account for the fluid displacement effects and reactions due to bubble accelerations.

Stabilized lowest order finite element approximation for linear three-field poroelasticity

Abstract: A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant approximation for the pressure and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump stabilization term to the mass conservation equation we ensure stability and avoid pressure oscillations. Importantly, the discretization leads to a symmetric linear system. For the fully discretized problem we prove existence and uniqueness, an energy estimate and an optimal a-priori error estimate, including an error estimate for the divergence of the fluid flux. Numerical experiments in 2D and 3D illustrate the convergence of the method, show the effectiveness of the method to overcome spurious pressure oscillations, and evaluate the added mass effect of the stabilization term.

A New Added Mass Method for Fluid-structure Interaction Analysis of Deep-water Bridge

Abstract: In order to calculate hydrodynamic pressure of piers with arbitrary cross-sections under earthquake, a new added mass method is presented. To accomplish this, the relation between fundamental frequency reduction rate and the ratio of added mass to structural mass per unit length is deduced. The relation is validated by using added mass from Morison equation. The fundamental frequency reduction rates of arbitrary section piers are available by utilizing the fluid element method in ANSYS, added masses of any piers are achieved according to the relation. Based on added mass data, the expressions of which can be proposed by curve fitting. The added mass expressions for two kinds of piers, circular and square, are suggested and compared with other two methods. Results show that the new method is accurate in both dynamic property calculation and harmonic response calculation. Practical application reveals that the new method is an accurate, efficient and adaptable way to evaluate hydrodynamic pressure under earthquake.

Impact forces on a vertical pile from plunging breaking waves

Abstract: There is at the moment some concern and uncertainty on slamming wave forces due to plunging breaking waves on truss structures as support structures for windmills in shallow water. Some work has been done on the wave slamming forces on single vertical and inclined piles, e.g. Goda et al. (1966), Sawaragi and Nochino (1984), Tanimoto et al. (1986) or Wienke and Oumeraci (2005). The slamming force is generally written as Fs = 0.5ρwCsDcb 2ληb, where Cs is a slamming force factor, cb is the breaking wave celerity (the water particle velocity is set equal to the wave celerity at breaking), ηb is the wave crest height at breaking and λ is the curling factor which indicates how much of the wave crest is active in the slamming force. For a vertical pile the value of λ has been reported to be in the range λ = 0.2 – 0.5. The value of Cs has been reported to be in the range Cs = π - 2π, while the duration of the slamming force has been reported to be in the range τ = (0.25D/cb) – (0.5D/cb). The test results of impact forces from plunging breaking waves show a considerable scatter. This is inherent due to the nature of the issue. In order to gain some more insight in the problem it was decided to carry out another study on the issue of impact forces from plunging waves on a vertical pile, Ros (2011), with a different test set-up, different instrumentation and different analysis methods than reported before. A pile with diameter D = 0.06 m is instrumented with six ring force transducers at different elevations. All the tests were run with regular waves with frequencies around 0.5 Hz or periods around T = 2.0 s. The wave heights were varied and the highest waves were around H = 30 cm at the pile with crest heights ηb = 25 cm. One of the problems with high intensity and short duration forces is to measure the actual force. Ideally one should have an almost indefinitely stiff measuring system. But then this system would be so stiff that the necessary sensitivity is lost. Hence acompromise is made such that what is measured is the response, which is not the force, due to dynamic effects on the mass-spring system the transducer represents. The challenge is then the analysis of the response to arrive at the force. We applied the Duhamel integral, which requires some knowledge on the wave slamming force, which is the parameter we are seeking. We have in our case assumed a triangular impulse load, similar to Goda et al. (1966), but with a duration similar to Wienke and Oumeraci (2005), and some rise time. The sampling frequency during testing was 20 kHz. The natural frequencies of oscillation of the individual transducers were measured during pluck tests to be 900 Hz in the beginning of the oscillations to about 250 Hz later. This could be due to different modes of oscillations of the transducer. During the slamming force tests the added mass will be changed during the impact, hence also the natural frequency of oscillations. The procedure of analysis was then to start with an assumed value of the force, Fo, and possible rise time and adjust them by trial-and-error such that the calculated value and the time location of the first response peak corresponded to the first peak of the measured response signal.

FSI Investigation on Stability of Downwind Sails with an Automatic Dynamic Trimming

Abstract: Gennakers are lightweight and flexible sails, used for downwind sailing configurations. Qualities sought for this kind of sail are propulsive force and dynamic stability. To simulate accurately the flow around such a sail, several problems need to be solved. Firstly, the structural code has to take into account cloth behavior, orientation and reinforcements. Flexibility is obtained by modeling wrinkles. Secondly, the fluid code needs to reproduce the atmospheric boundary layer as an input boundary condition, and be able to simulate separation. Thirdly, fluid-structure interaction (FSI) is strong due to the lightness and the flexibility of the structure. The added mass is three orders of magnitude greater than the mass of the sail, and large structural displacement occurs, which makes the coupling between the two solvers difficult to achieve. Finally, the problem is unsteady, and dynamic trimming is important to the simulation of spinnakers [4]. The main objective is to use numerical simulations to model spinnakers, in order to predict both propulsive force and sail dynamic stability. Recent developments [2] are used to solve these problems, using a finite element program dedicated to sails and rig simulations coupled with a RANSE solver. The FSI coupling is done through a quasi-monolithic method. An ALE formulation is used, hence the fluid mesh follows the structural deformation while keeping the same topology. The fluid mesh deformation is carried out with a fast, robust and parallelized method based on the propagation of the deformation state of the sail boundary fluid faces [3]. Tests are realized on a complete production chain: a sail designer from Incidences has designed two different shapes of an IMOCA60 spinnaker with the SailPack software. An automatic procedure was developed to transfer data from Sailpack to a structure input file taking into account the orientation of sailcloth and reinforcements. The same automatic procedure is used for both spinnakers, in order to compare dynamic stability and propulsion forces. Then a new method is developed to quantify the stability of a downwind sail.

Dynamic Response of a Pressurized Frame-Membrane Lunar Structure with Regolith Cover Subjected to Impact Load

Abstract: A three-dimensional internally pressurized frame-membrane structure covered with regolith shielding has been proposed as a possible lunar habitat. This paper presents results from the static, frequency, and dynamic impact analysis of the structure using a nonlinear (large deformation) finite-element technique. The results are presented, taking into account the effects of the added mass of the regolith and stress stiffening because of the applied internal pressurization load. The impact loading is analytically derived by considering the impact of a moving object/debris/projectile hitting the midpoint of one of the frame members at the crest of the structure. For the frequency analysis, the results show that both pressurization and added regolith mass affect the frequency and mode-shape characteristics, where the effects of the added mass of the regolith are observed to be substantially larger than the effects of pressurization. For the static and dynamic analyses, the midspan impact results show th...

Control of an underactuated underwater vehicle manipulator system in the presence of parametric uncertainty and disturbance

Abstract: In this paper, an underactuated underwater vehicle manipulator system (u-UVMS) carrying 6-DOF manipulator system is modeled considering hydrostatic forces and hydrodynamic effects such as added mass, lift, drag and side forces. The shadowing effects of the bodies on each other are also taken into account when computing the hydrodynamic forces. The system equations of motion are then derived using Newton-Euler formulation including the thruster dynamics. Next, an inverse dynamics control algorithm is applied for the end-effector trajectory tracking of the u-UVMS. Simulation results illustrate that the control method is applicable to underactuated systems and is effective even in the presence of parametric uncertainty and disturbing current force.