Showing papers on "Added mass published in 2010"

Free-Locomotion of Underwater Vehicles Actuated by Ionic Polymer Metal Composites

Abstract: In this paper, we develop a modeling framework for studying free-locomotion of biomimetic underwater vehicles propelled by vibrating ionic polymer metal composites (IPMCs). The motion of the vehicle body is described using rigid body dynamics in fluid environments. Hydrodynamic effects, such as added mass and damping, are included in the model to enable a thorough description of the vehicle's surge, sway, and yaw motions. The time-varying actions exerted by the vibrating IPMC on the vehicle body, including thrust, lift, and moment, are estimated by combining force and vibration measurements with reduced order modeling based on modal analysis. The model predictions are validated through experimental results on a miniature remotely controlled fish-like robotic swimmer.

Modeling and experimental verification of proof mass effects on vibration energy harvester performance

Abstract: An electromechanically coupled model for a cantilevered piezoelectric energy harvester with a proof mass is presented. Proof masses are essential in microscale devices to move device resonances towards optimal frequency points for harvesting. Such devices with proof masses have not been rigorously modeled previously; instead, lumped mass or concentrated point masses at arbitrary points on the beam have been used. Thus, this work focuses on the exact vibration analysis of cantilevered energy harvester devices including a tip proof mass. The model is based not only on a detailed modal analysis, but also on a thorough investigation of damping ratios that can significantly affect device performance. A model with multiple degrees of freedom is developed and then reduced to a single-mode model, yielding convenient closed-form normalized predictions of device performance. In order to verify the analytical model, experimental tests are undertaken on a macroscale, symmetric, bimorph, piezoelectric energy harvester with proof masses of different geometries. The model accurately captures all aspects of the measured response, including the location of peak-power operating points at resonance and anti-resonance, and trends such as the dependence of the maximal power harvested on the frequency. It is observed that even a small change in proof mass geometry results in a substantial change of device performance due not only to the frequency shift, but also to the effect on the strain distribution along the device length. Future work will include the optimal design of devices for various applications, and quantification of the importance of nonlinearities (structural and piezoelectric coupling) for device performance.

Beam Shape Optimization for Power Harvesting

Abstract: A problem in piezoelectric bimorph energy harvesting is to generate the most power with limits in system mass. The authors propose a new approach: to change the shape of the beam to concentrate the strain in sections of the beam where it can contribute the most to transduction. A vibration model of beams with non-uniform width is developed and validated with shaker table tests. Three beams with different shapes are tested over a wide band, encompassing the lowest two modes of vibration. An optimal beam shape is calculated using a heuristic optimization code and the attributes of this optimal beam are discussed. Then, beam shapes are optimized to allow for increased base excitation and constrained by maximum root strain. Finally, the tip mass-to-beam mass ratio is studied parametrically, correlating increased transduction with increased beam mass.

Thermal Excitation and Piezoresistive Detection of Cantilever In-Plane Resonance Modes for Sensing Applications

Abstract: Thermally excited and piezoresistively detected bulk-micromachined cantilevers vibrating in their in-plane flexural resonance mode are presented. By shearing the surrounding fluid rather than exerting normal stress on it, the in-plane mode cantilevers exhibit reduced added fluid mass effects and improved quality factors in a fluid environment. In this letter, different cantilever geometries with in-plane resonance frequencies from 50 kHz to 2.2 MHz have been tested, with quality factors as high as 4200 in air and 67 in water.

Robust and provably second-order explicit-explicit and implicit-explicit staggered time-integrators for highly non-linear compressible fluid-structure interaction problems

Abstract: An explicit–explicit staggered time-integration algorithm and an implicit–explicit counterpart are presented for the solution of non-linear transient fluid–structure interaction problems in the Arbitrary Lagrangian–Eulerian (ALE) setting. In the explicit–explicit case where the usually desirable simultaneous updating of the fluid and structural states is both natural and trivial, staggering is shown to improve numerical stability. Using rigorous ALE extensions of the two-stage explicit Runge–Kutta and three-point backward difference methods for the fluid, and in both cases the explicit central difference scheme for the structure, second-order time-accuracy is achieved for the coupled explicit–explicit and implicit–explicit fluid–structure time-integration methods, respectively, via suitable predictors and careful stagings of the computational steps. The robustness of both methods and their proven second-order time-accuracy are verified for sample application problems. Their potential for the solution of highly non-linear fluid–structure interaction problems is demonstrated and validated with the simulation of the dynamic collapse of a cylindrical shell submerged in water. The obtained numerical results demonstrate that, even for fluid–structure applications with strong added mass effects, a carefully designed staggered and subiteration-free time-integrator can achieve numerical stability and robustness with respect to the slenderness of the structure, as long as the fluid is justifiably modeled as a compressible medium. Copyright © 2010 John Wiley & Sons, Ltd.

Design study of piezoelectric energy-harvesting devices for generation of higher electrical power using a coupled piezoelectric-circuit finite element method

Abstract: This paper presents a design study on the geometric parameters of a cantilever-based piezoelectric energy-harvesting devices (EHD), which harvest energy from motion (vibration), for the purpose of scavenging more energy from ambient vibration energy sources. The design study is based on the coupled piezoelectric-circuit finite element method (CPCFEM), previously presented by Dr. Zhu. This model can calculate the power output of piezoelectric EHDS directly connected to a load resistor and is used in this paper to obtain the following simulation results for variations in geometric parameters such as the beam length, width and thickness, and the mass length, width, and height: 1) the current flowing through and the voltage developed across the load resistor, 2) the power dissipated by the resistor and the corresponding vibrational displacement amplitude, and 3) the resonant frequency. By studying these results, straightforward design strategies that enable the generation of more power are obtained for each geometric parameter, and a physical understanding of how each parameter affects the output power is given. It is suggested that, in designing with the aim of generating more power, the following strategies be used: 1) for the beam, a shorter length, larger width, and lower ratio of piezoelectric layer thickness to total beam thickness are preferred in the case of a fixed mass; 2) for the mass, a shortened mass length and a higher mass height are preferred in the case of variation in the mass length and the mass height with mass width and mass value remain fixed, and a wider width and small mass height are preferred in the case of variation in mass width and height (mass length and value remain fixed; and 3) for the case of a fixed total length, a shorter beam length and longer mass length are preferred. With the design strategies, output powers from the device can reach above 1 to 2 mW/cm3, much higher than the 200 ?W/cm3 currently achieved in the published literature. This is an encouraging prospect for enabling a wider range of applications of the EHDs. In addition, physical insights into how each parameter influences output power are also discussed in detail.

The calibration of carbon nanotube based bionanosensors

Abstract: We derive the calibration constants necessary for using single-walled carbon nanotubes (CNTs) as nanoscale mass sensors. The CNT resonators are assumed to be either in cantilevered or in bridged configurations. Two cases, namely, when the added mass can be considered as a point mass and when the added mass is distributed over a larger area is considered. Closed-form transcendental equations have been derived for the frequency shift due to the added mass. Using the energy principles, generalized nondimensional calibration constants have been derived for an explicit relationship between the added mass and the frequency shift. A molecular mechanics model based on the universal force field potential is used to validate the new results presented. The results indicate that the distributed nature of the mass to be detected has considerable effect on the performance of the sensor.

Position and mass determination of multiple particles using cantilever based mass sensors

Abstract: Resonant microcantilevers are highly sensitive to added masses and have the potential to be used as mass-spectrometers. However, making the detection of individual added masses quantitative requires the position determination for each added mass. We derive expressions relating the position and mass of several added particles to the resonant frequencies of a cantilever, and an identification procedure valid for particles with different masses is proposed. The identification procedure is tested by calculating positions and mass of multiple microparticles with similar mass positioned on individual microcantilevers. Excellent agreement is observed between calculated and measured positions and calculated and theoretical masses.

Dissipation and oscillatory solvation forces in confined liquids studied by small-amplitude atomic force spectroscopy

Abstract: We determine conservative and dissipative tip–sample interaction forces from the amplitude and phase response of acoustically driven atomic force microscope (AFM) cantilevers using a non-polar model fluid (octamethylcyclotetrasiloxane, which displays strong molecular layering) and atomically flat surfaces of highly ordered pyrolytic graphite. Taking into account the base motion and the frequency-dependent added mass and hydrodynamic damping on the AFM cantilever, we develop a reliable force inversion procedure that allows for extracting tip–sample interaction forces for a wide range of drive frequencies. We systematically eliminate the effect of finite drive amplitudes. Dissipative tip–sample forces are consistent with the bulk viscosity down to a thickness of 2–3 nm. Dissipation measurements far below resonance, which we argue to be the most reliable, indicate the presence of peaks in the damping, corresponding to an enhanced 'effective' viscosity, upon expelling the last and second-last molecular layer.

A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

Abstract: We present a formulation for coupled solutions of fluid and body dynamics in problems of biolocomotion. This formulation unifies the treatment at moderate to high Reynolds number with the corresponding inviscid problem. By a viscous splitting of the Navier–Stokes equations, inertial forces from the fluid are distinguished from the viscous forces, and the former are further decomposed into contributions from body motion in irrotational fluid and ambient fluid vorticity about an equivalent stationary body. In particular, the added mass of the fluid is combined with the intrinsic inertia of the body to allow for simulations of bodies of arbitrary mass, including massless or neutrally buoyant bodies. The resulting dynamical equations can potentially illuminate the role of vorticity in locomotion, and the fundamental differences of locomotion in real and perfect fluids.

Bio-mass sensor using an electrostatically actuated microcantilever in a vacuum microchannel

Abstract: The present work focuses on the dynamic analysis of a bio-mass sensor. The main component of this microsystem is a cantilever beam placed in a vacuum microchannel with a proof mass attached to its end. The rigid mass is coupled to an electrode to capacitively drive the beam. The operating principle is based on detecting the shift in the resonance frequency of the microbeam to measure the mass of a cell deposited on the sensing tip. We show that the present system enables easy detection and measurement of the added mass. To gain insight into the microsystem sensitivity to variations in its parameters, such as the gap distance and tip mass, as well as the use of higher-order modes, we examine their effects on the variation of the resonance frequency shift with respect to the added mass.

Vortex-induced vibration of a rising and falling cylinder

Abstract: In this study, we investigate the dynamics of a freely rising and falling cylinder. This is, in essence, a vortex-induced vibration (VIV) system comprising both transverse (Y) and streamwise (X) degrees-of-freedom (d.o.f.), but with zero spring stiffness and zero damping. This problem represents a limiting case among studies in VIV, and is an extension of recent research of elastically mounted bodies having very low spring stiffness, as well as bodies with very low mass and damping. We find that if the mass ratio (where m* = cylinder mass/displaced fluid mass) is greater than a critical value, m*crit = 0.545, the body falls or rises with a rectilinear trajectory. As the mass ratio is reduced below m*crit = 0.545, the cylinder suddenly begins to vibrate vigorously and periodically, with a 2P mode of vortex formation, as reported in the preliminary study of Horowitz & Williamson (J. Fluids Struct. vol. 22, 2006, pp. 837–843). The similarity in critical mass between freely rising and elastically mounted bodies is unexpected, as it is known that the addition of streamwise vibration can markedly affect the response and vortex formation in elastically mounted systems, which would be expected to modify the critical mass. However, we show in this paper that the similarity in vortex formation mode (2P) between the freely rising body and the elastically mounted counterpart is consistent with a comparable phase of vortex dynamics, strength of vortices, amplitudes and frequencies of motion and effective added mass (CEA). All of these similarities result in comparable values of critical mass. The principal fact that the 2P mode is observed for the freely rising body is an interesting and consistent result; based on the previous VIV measurements, this is the only mode out of the known set {2S, 2P, 2T} to yield negative effective added mass (CEA < 0), which is a condition for vibration of a freely rising body. In this paper, we deduce that there exists only one possible two degree-of-freedom elastically mounted cylinder system, which can be used to predict the dynamics of freely rising bodies. Because of the symmetry of the vortex wake, this system is one for which the natural frequencies are fNX = 2fNY. Although this seems clear in retrospect, previous attempts to predict critical mass did not take this into account. Implementing such an elastic system, we are able to predict vibration amplitudes and critical mass (m*crit = 0.57) for a freely rising cylinder in reasonable agreement with direct measurements for such a rising body, and even to predict the Lissajous figures representing the streamwise–transverse vibrations for a rising body with very small mass ratios (down to m* = 0.06), unobtainable from our direct measurements.

Time-Domain Simulations of Radiation and Diffraction Forces

Abstract: Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

Experimental Study of Impact on Composite Plates with Fluid-Structure Interaction

Abstract: The transient dynamic response of composite structures under water is affected by Fluid Structure Interaction (FSI), which results in an added mass effect as well as damping. Because the density of composites is comparable to that of water, the added mass effect becomes even more critical to the transient dynamic response of composites in water. In this study, an experimental testing set-up was designed and fabricated, and testing was conducted to investigate FSI effects on composite laminate plates immersed in fluid and subjected to impact loading. Square composite laminates made of carbon fiber weave and vinyl ester resin were subjected to impact loading using a specially developed vertical drop-weight testing machine. The composite samples were fitted with gages to provide time-history on strains and impact forces generated during impact. Impact tests were performed on four-side clamped laminate plates in airbacked wet, water-backed wet, and dry environments. The results showed non-uniform effects on transient responses of wet composites with FSI. Generally, wet impacts on composite plates increased both transient impact forces and strains significantly compared to dry impacts under the same impact mass and velocity condition. The findings of this study will provide a better understanding for use of composite materials in underwater structural applications where impact loading is expected.

A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Oil Seal Rings

Abstract: Squeeze film damper (SFD) designs typically implement supply grooves to ensure adequate lubricant flow into the film lands. Oil seal rings, of land film clearance c, also incorporate short and shallow grooves (length ≤ 30c, depth ≤ 15c) to reduce cross-coupled stiffnesses, thus promoting dynamic stability without a penalty in increased leakage. However, extensive experimental results in the archival literature demonstrate that grooves do not reduce the force coefficients as much as theory predicts. A common assumption is that deep grooves do not influence a damper or oil seal ring forced response. However, unexpected large added mass coefficients, not adequately predicted, appear to be common in many tested SFD and oil seal configurations. In the case of oil seals, experiments demonstrate that circumferential grooves do reduce cross-coupled stiffnesses but to a lesser extent than predictions would otherwise indicate. A linear fluid inertia bulk-flow model for analysis of the forced response of SFDs and oil seal configurations with multiple grooves is advanced. A perturbation analysis for small amplitude journal motions about a centered position yields zeroth and first-order flow equations at each flow region (lands and grooves). At a groove region, a groove effective depth d η , differing from its actual physical value, is derived from qualitative observations of the laminar flow pattern through annular cavities. The boundary conditions at the inlet and exit planes depend on the actual seal or SFD configuration. Integration of the resulting first-order pressure fields on the journal surface yields the force coefficients (stiffness, damping, and inertia). Current model predictions are in excellent agreement with published test force coefficients for a grooved SFD and a grooved oil seal. The results confirm that large added mass coefficients arise from the flow interactions between the feed/discharge grooves and film lands in the test elements. Furthermore, the predictions, benchmarking experimental data, corroborate that short length inner-land grooves in an oil seal do not isolate the pressure fields of adjacent film lands and hence contribute greatly to the forced response of the mechanical element.

Mechanisms of non-modal energy amplification in channel flow between compliant walls

Abstract: The mechanisms leading to large transient growth of disturbances for the flow in a channel with compliant walls are investigated. The walls are modelled as thin spring-backed plates, and the flow dynamics is modelled using the Navier–Stokes equations linearized round the Poiseuille profile. Analysis for streamwise invariant perturbations show that this fluid-structure system can sustain oscillatory energy evolution of large amplitude, in the form of spanwise standing waves. Such waves are related to the travelling waves which a free wall can support, modified to account for an ‘added mass’ effect. Simple scaling arguments are found to provide results in excellent agreement with computations of optimal disturbances, for low-to-moderate values of the stiffness parameter characterizing the compliant surface.

Momentum evolution of ejected and entrained fluid during laminar vortex ring formation

Abstract: The evolution of total circulation and entrainment of ambient fluid during laminar vortex ring formation has been addressed in a number of previous investigations. Motivated by applications involving propulsion and fluid transport, the present interest is in the momentum evolution of entrained and ejected fluid and momentum exchange among the ejected, entrained fluid and added mass during vortex ring formation. To this end, vortex rings are generated numerically by transient jet ejection for fluid slug length-to-diameter (L/D) ratios of 0.5–3.0 using three different velocity programs [trapezoidal, triangular negative slope (NS), and positive slope (PS)] at a jet Reynolds number of 1,000. Lagrangian coherent structures (LCS) were utilized to identify ejected and entrained fluid boundaries, and a Runge-Kutta fourth order scheme was used for advecting these boundaries with the numerical velocity data. By monitoring the center of mass of these fluid boundaries, momentum of each component was calculated and related to the total impulse provided by the vortex ring generator. The results demonstrate that ejected fluid exchanges its momentum mostly with added mass during jet ejection and that the momentum of the entrained fluid at jet termination was < 11% of the total ring impulse in all cases except for the triangular NS case. Following jet termination, momentum exchange was observed between ejected and entrained fluid yielding significant increase in entrained fluid’s momentum. A performance metric was defined relating the impulse from over-pressure developed at the nozzle exit plane during jet ejection to the flow evolution, which increased preferentially with L/D over the range considered. An additional benefit of this study was the identification of the initial (i.e., before jet initiation) location of the fluid to be entrained into the vortex ring.

Dynamically tuned wave energy converter

Abstract: A wave energy converter comprises a pitching floating vessel and means for converting the pitching motion to electrical power. By varying the distribution of the ballast mass in the vessel and by varying the vessel's immersed length the moments of inertia of mass and of added mass are varied and wave-bridging is controlled. The immersed length of the vessel is varied by changing the draft of a v-shaped hull. Roll and yaw are suppressed by a vertical fin held at a substantial depth Inside the vessel is a compact pendulum that is a combination of tracked and folding pendulums. Both vessel and compact pendulum can be simultaneously and dynamically tuned over the range of periods that characterize high-energy ocean swells.

Added-Mass Effect in Modeling of Cilia-Based Devices for Microfluidic Systems

Abstract: This article shows that the added mass due to fluid-structure interaction significantly affects the vibrational dynamics of cilia-based (vibrating cantilever-type) devices for handling microscale fluid flows. Commonly, the hydrodynamic interaction between the cilia-based actuators and fluid is modeled as a drag force that results in damping of the cilia motion. Our main contribution is to show that such damping effects cannot explain the substantial reduction in the resonant-vibrational frequency of the cilia actuator operating in liquid when compared with the natural frequency of the cilia in air. It is shown that an added-mass approach (that accounts for the inertial loading of the fluid) can explain this reduction in the resonant-vibrational frequency when operating cantilever-type devices in liquids. Additionally it is shown that the added-mass effect can explain why the cilia-vibration amplitude is not substantially reduced in a liquid by the hydrodynamic drag force. Thus, this article shows the need to model the added-mass effect, both theoretically and by using experimental results.

Variation of Heave Added Mass and Damping Near Seabed

Abstract: During installation of subsea structures such as mud mats, the tension in crane wires can experience spikes when the structure is near the seabed. It is hypothesized that such spikes may be caused by the structure undergoing resonant oscillations, which in turn may be due to changes in added mass and damping near the seabed. Such motions can cause hardship for operators as they interfere with precise positioning during installation. With increasing exploration and production in deep and remote fields, the size and weight of subsea equipments are continuously increasing. Installation operations such as lifting and lowering, positioning of the object require good knowledge of the hydrodynamic coefficients. Following on ideas used in Norwegian offshore, the mud mat is modeled as a circular disk. Experiments are conducted on an oscillating solid disk of diameter and thickness 200 mm and 2 mm respectively. The heave oscillations are forced by a programmable actuator, at amplitudes varying from 1–56 mm and frequencies from 1.0–1.8 Hz. The elevation ‘h’ of the disk from the mean seabed is varied from 0.2–2 times the disk radius. The forces on the disk are measured using a submersible high-sensitivity load cell. The motions of the disk are restricted to axial (heave) direction, and are measured with a displacement transducer. The measured forces and displacement are analyzed using a Fourier Transform algorithm to separate the added mass and damping effects. The authors have found similar trends in the hydrodynamic behavior of a disk approaching the seabed to what was found when the disk approached the free surface in Wadhwa & Thiagarajan [1]. The added mass and damping coefficients were found to increase with increasing KC, as well as with increasing proximity to the seabed. Another noticeable feature of the experiments was the cavity formation underneath the oscillating structure. The width of the cavity was about 3–4 times the radius of the disk and depth was about one third/fourth of the radius of the disk. The size of the cavity and the increase in hydrodynamic forces near the seabed suggest the importance of knowledge of hydrodynamic behavior near the seabed.Copyright © 2010 by ASME

Calculation of added mass of a vehicle running with cavity

Abstract: A numerical method is developed to obtain the added mass coefficients of a vehicle running with cavity in numerical simulation for the multiphase flow of the vehicle which is imposed an added vibration and analyzing its hydrodynamic loads. The method is verified through the cases of non-cavitating sphere and ellipsoid. The changing rule of the added mass of a sphere during water exit is gained. Then the influence of cavitation on the added mass of a cylinder is studied. The results show that λ 11 , λ 22 , λ 26 , λ 66 $ all decrease as the cavitation number reduces and the length of the attached cavity increases. There is almost a linear relationship between the cavity length and λ 22 . The base cavity has great influence on λ 11 $, its contribution decreases more than 60%, when the cavitation number changes from 0.6 to 0.2.

Some aspects of load-rate sensitivity in visco-elastic microplane material model

Abstract: The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non- linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a nonlinear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.