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Showing papers on "Added mass published in 2004"


Journal ArticleDOI
TL;DR: In this article, the added mass method was extended to allow simultaneous calibration of both the normal and torsional spring constants of atomic force microscope cantilevers, and the validity and applicability of the unloaded resonance method when a mass is attached to the free end of the cantilever was investigated.
Abstract: Two methods commonly used to measure the normal spring constants of atomic force microscope cantilevers are the added mass method of Cleveland et al. [J. P. Cleveland et al., Rev. Sci. Instrum. 64, 403 (1993)], and the unloaded resonance technique of Sader et al. [J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999)]. The added mass method involves measuring the change in resonant frequency of the fundamental mode of vibration upon the addition of known masses to the free end of the cantilever. In contrast, the unloaded resonance technique requires measurement of the unloaded resonant frequency and quality factor of the fundamental mode of vibration, as well as knowledge of the plan view dimensions of the cantilever and properties of the fluid. In many applications, such as frictional force microscopy, the torsional spring constant is often required. Consequently, in this article, we extend both of these techniques to allow simultaneous calibration of both the normal and torsional spring constants. We also investigate the validity and applicability of the unloaded resonance method when a mass is attached to the free end of the cantilever due to its importance in practice.

505 citations


Journal ArticleDOI
TL;DR: A modified quasi-steady model is developed that can account for the varying magnitudes of the lift and drag coefficients and may also resolve discrepancies in past measurements of wing performance based on translational and revolving motion.
Abstract: Recent studies have demonstrated that a quasi-steady model closely matches the instantaneous force produced by an insect wing during hovering flight. It is not clear, however, if such methods extend to forward flight. In this study we use a dynamically scaled robotic model of the fruit fly Drosophila melanogaster to investigate the forces produced by a wing revolving at constant angular velocity while simultaneously translating at velocities appropriate for forward flight. Because the forward and angular velocities were constant wing inertia was negligible, and the measured forces can be attributed to fluid dynamic phenomena. The combined forward and revolving motions of the wing produce a time-dependent free-stream velocity profile, which suggests that added mass forces make a contribution to the measured forces. We find that the forces due added mass make a small, but measurable, component of the total force and are in excellent agreement with theoretical values. Lift and drag coefficients are calculated from the force traces after subtracting the contributions due to added mass. The lift and drag coefficients, for fixed angle of attack, are not constant for non-zero advance ratios, but rather vary in magnitude throughout the stroke. This observation implies that modifications of the quasi-steady model are required in order to predict accurately the instantaneous forces produced during forward flight. We show that the dependence of the lift and drag coefficients upon advance ratio and stroke position can be characterized effectively in terms of the tip velocity ratio – the ratio of the chordwise components of flow velocity at the wing tip due to translation and revolution. On this basis we develop a modified quasi-steady model that can account for the varying magnitudes of the lift and drag coefficients. Our model may also resolve discrepancies in past measurements of wing performance based on translational and revolving motion.

166 citations


Journal ArticleDOI
TL;DR: In this article, a detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented, and a model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam.
Abstract: A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

165 citations


Journal ArticleDOI
TL;DR: In this paper, a finite difference method is employed to solve the incompressible Navier-Stokes equations in the primitive-variables formulation, and test cases were used to guide selection of the size of flow domain, numerical parameters, and to verify that the resultant method was both convergent and accurate.

100 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical and experimental study of the response of a damaged Euler-Bernoulli beam traversed by a moving mass is presented, where damage is modelled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics.

91 citations


Journal ArticleDOI
TL;DR: In this paper, the transverse Vortex-Induced Vibrations of a long (length to diameter ratio, L/D=1544), flexible pipe, that was subjected to a uniform current profile (Reynolds number, Re=2.84×105) have been simulated using a strip theory Computational Fluid Dynamics model.
Abstract: The transverse Vortex-Induced Vibrations of a long (length to diameter ratio, L/D=1544), flexible pipe, that was subjected to a uniform current profile (Reynolds number, Re=2.84×105) have been simulated using a strip theory Computational Fluid Dynamics model. The pipe's mass ratio (the ratio of the pipe's mass to the mass of fluid displaced by it) was varied between 1.0 and 3.0 in order to study its effect upon the vibrational behaviour of the pipe. Despite the inflow current being uniform the pipe was observed to vibrate multi-modally. Furthermore, all of the excited modes vibrated at the excitation (Strouhal) frequency. The fluid, via its added mass, was found to be able to excite modes whose natural frequencies differed from the excitation frequency. This ability was observed to decrease with increasing mass ratio.

83 citations


Journal ArticleDOI
TL;DR: In this article, a nonlinear time-domain strip theory formulation for dynamic positioning and low-speed manoeuvring is presented, which can be used to compute the potential coefficients (added mass and potential damping) and the exciting wave loads (Froude-Krylov and diffraction forces).
Abstract: This paper presents a computer effective nonlinear time-domain strip theory formulation for dynamic positioning (DP) and low-speed manoeuvring. Strip theory or 2D potential theory, where the ship is divided in 20 to 30 cross sections, can be used to compute the potential coefficients (added mass and potential damping) and the exciting wave loads (Froude-Krylov and diffraction forces). Commercially available programs are ShipX (VERES) by Marintek (Fathi, 2004) and SEAWAY by Amarcon (Journee & Adegeest, 2003), for instance. The proposed method can easily be extended to utilize other strip theory formulations or 3-D potential programs like WAMIT (2004). The frequency dependent potential damping, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using the state-space formulation of Kristiansen & Egeland (2003). The separation of the vessel model into a low-frequency model (represented by zero- frequency added mass and damping) and a wave-frequency model (represented by motion transfer functions or RAOs), which is commonly used for simulation, is hence made superfluous. Transformations of motions and coefficients between different coordinate systems and origins, i.e. data frame, hydrodynamic frame, body frame, inertial frame etc., are put into the rigid framework of Fossen (1994, 2002). The kinematic equations of motion are formulated in a compact nonlinear vector representation and the classical kinematic assumption that the Euler angles are small is removed. This is important for computation of accurate control forces at higher roll and pitch angles. The hydrodynamic forces in the steadily translating hydrodynamic reference frame (equilibrium axes) are, however, assumed tobe linear. Recipes for computation of retardation functions are presented and frequency dependent viscous damping is included. Emphasis is placed on numerical computations and representation of the data from VERES and SEAWAY in Matlab/Simulink. For this purpose a Simulink add-in to the Marine Systems Simulator (MSS) at the Norwegian University of Science and Technology has been developed (Fossen et al., 2004).

77 citations


Journal ArticleDOI
TL;DR: In this article, the problem of assigning natural frequencies to a multi-degree-of-freedom undamped system by an added mass connected by one or more springs is addressed, where the added mass and stiffnesses are determined using receptances from the original system.

65 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed a quantitative technique to estimate the rise velocity of an air bubble in coarse porous media, based on the macroscopic balance equation for forces acting on a bubble rising in a porous medium.
Abstract: [1] The rise velocity of injected air phase from the injection point toward the vadose zone is a critical factor in in-situ air sparging operations. It has been reported in the literature that air injected into saturated gravel rises as discrete air bubbles in bubbly flow of air phase. The objective of this study is to develop a quantitative technique to estimate the rise velocity of an air bubble in coarse porous media. The model is based on the macroscopic balance equation for forces acting on a bubble rising in a porous medium. The governing equation incorporates inertial force, added mass force, buoyant force, surface tension and drag force that results from the momentum transfer between the phases. The momentum transfer terms take into account the viscous as well as the kinetic energy losses at high velocities. Analytical solutions are obtained for steady, quasi-steady, and accelerated bubble rise velocities. Results show that air bubbles moving up through a porous medium equilibrate after a short travel time and very short distances of rise. It is determined that the terminal rise velocity of a single air bubble in an otherwise water saturated porous medium cannot exceed 18.5 cm/s. The theoretical model results compared favorably with the experimental data reported in the literature. A dimensional analysis conducted to study the effect of individual forces indicates that the buoyant force is largely balanced by the drag force for bubbles with an equivalent radius of 0.2–0.5 cm. With increasing bubble radius, the dimensionless number representing the effect of the surface tension force decreases rapidly. Since the total inertial force is quite small, the accelerated bubble rise velocity can be approximated by the terminal velocity.

58 citations


Journal ArticleDOI
TL;DR: In this article, the motion and drift force of a floating OWC (oscillating water column) wave energy device in regular waves were studied taking account of the oscillating surface-pressure due to the pressure drop across the duct of the air chamber.

44 citations


Journal ArticleDOI
TL;DR: In this paper, a boundary integral-equation method was developed for directly computing the velocity potential on the wetted surface of a body which is immersed in both the upper and lower layers as a general case.
Abstract: A linearized 2-D radiation problem was considered for a general floating body in a two-layer fluid of finite depth. A boundary integral-equation method was developed for directly computing the velocity potential on the wetted surface of a body which is immersed in both the upper and lower layers as a general case. To do this, appropriate time-harmonic Green’s functions were derived, and an efficient numerical method of evaluating those functions is proposed. Based on Green’s theorem, hydrodynamic relations such as the energy-conservation principle were derived theoretically for a case of finite depth, and we confirm that those relations are satisfied numerically with very good accuracy. Experiments were also carried out using water and isoparaffin oil as the two fluids and a Lewis-form body. Measured results for the added mass, the damping coefficient, and the amplitude of the generated waves are compared with the computed results, and a favorable agreement is found.

Journal ArticleDOI
TL;DR: In this article, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall, where an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch.

Journal ArticleDOI
TL;DR: In this article, a radiation and diffraction boundary value problem is investigated, which arises from the interaction of linear water waves with a freely floating rectangular structure in a semi-infinite fluid domain of finite water depth with the leeward boundary being a vertical wall.

Journal ArticleDOI
TL;DR: In this article, a new method is proposed for the experimental determination of the longitudinal and lateral hydrodynamic coefficients of a low-speed UUV, which is a development of the classical free-decay test.

Journal ArticleDOI
TL;DR: In this paper, the authors developed a dynamic analysis program for SFT and investigated dynamic response characteristics of SFT subjected to external environmental wave load, where the structure is modeled with 3-dimensional beam element and the fluid is assumed incompressible, invicid and irrotational and is analyzed by boundary element method applying linear potential theory.
Abstract: Submerged Floating Tunnel (SFT) is a new structural concept for crossing water. The purpose of the present study is to develop a dynamic analysis program for SFT and investigate dynamic response characteristics of SFT subjected to external environmental wave load. The structure is modeled with 3-dimensional beam element and the fluid is assumed incompressible, invicid and irrotational and is analysed by boundary element method applying linear potential theory. Using the hydrodynamic coefficients of added mass, radiation damping and wave excitation force obtained by solving 2-dimensional diffraction problem, 3-dimensional structural analysis of SFT is performed in time domain and results are presented. The depth effect of SFT location on the hydrodynamic coefficients are illustrated as well as the effect of the frequency dependency of the coefficients which is taken into account in the analysis program.

01 Jan 2004
TL;DR: In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall, and numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping ofthe cylinder.
Abstract: In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem ofa cylinder in f ofa vertical wall is transf ormed into the equivalent problem ofdouble cylinders in unbounded fluid domain. Consequently, an analytical method ofeigenf unction expansion is adopted to calculate the radiation ofthe cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences ofthe distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping ofthe cylinder. It is shown that added mass and damping ofthe cylinder in f ofa vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall. # 2003 Elsevier Ltd. All rights reserved.

Journal ArticleDOI
TL;DR: In this article, the Hamilton's principle was used to derive the governing differential equations for the coupled bending-bending vibration of a rotating beam with a tip mass, arbitrary pretwist, an elastically restrained root, and rotating at a constant angular velocity.

Journal ArticleDOI
TL;DR: In this paper, the effects of the caisson on the cylinder's hydrodynamic coefficients and exciting forces are derived in the presence of an incident linear wave by use of an eigenfunction expansion approach.

Proceedings ArticleDOI
01 Jan 2004
TL;DR: In this paper, the authors proposed a light-weight solution to the complete force and moment balancing of linkages based on the combination of a counterweight and a separate counter-rotation into a single element.
Abstract: Shaking forces and moments are often undesired. Complete balancing of these effects usually is associated with considerable additional mass and inertia. This paper proposes a light-weight solution concept to the complete force and moment balancing of linkages based on the combination of a counterweight and a separate counter-rotation into a single element. This element will be called a counter-rotary counterweight (CRCW). It will be shown that for a 1dof rotatable link a reduction of added mass by about 40% and a reduction by about 20% of added inertia have been achieved, as compared to a standard solution, after optimization of both mechanisms for minimal inertia. Generalization of the proposed principle is also discussed.Copyright © 2004 by ASME

Journal ArticleDOI
TL;DR: In this paper, a free-falling rigid sphere in a quiescent incompressible newtonian fluid, placed in an oscillating frame, is analyzed and compared with those obtained from theoretical approaches.
Abstract: The present work presents an experimental study on a free-falling rigid sphere in a quiescent incompressible newtonian fluid, placed in an oscillating frame. The goal of this investigation is to examine the effect of the history force acting on the sphere at small Reynolds numbers (Re≤2.5) and finite Strouhal numbers (1≤Sl≤20). The particle trajectory is measured by using a high-speed video camera and modern techniques of image processing. The average terminal velocity, the oscillation magnitude, and the phase shift with the oscillating frame are measured and compared with those obtained from theoretical approaches. The comparison is made by solving the equation of motion of the sphere with and without the history force. In addition to the significant role that this force plays in the momentum balance, it was found that the correction of the added mass force and the history force by the empirical coefficients of Odar and Hamilton (J Fluid Mech 18:302–314, 1964; J Fluid Mech 25:591–592, 1966) are not necessary in our Re and Sl ranges. The added mass is the same as that obtained by the potential flow theory and the history force is well predicted by the Basset expression (Treatise on hydrodynamics, 1888).

Journal ArticleDOI
TL;DR: In this article, a boundary integral equation method was used in conjunction with the method of images, in order to investigate the dynamic behavior of fluid-structure structures in terms of the wet frequency and associated mode shapes.

Journal ArticleDOI
TL;DR: In this article, the hydrodynamics of a rigid, weakly permeable sphere undergoing translational oscillations in an incompressible Newtonian fluid were determined using homogenization and scaling arguments, showing that the flow inside the sphere may be modeled by Darcy's law and that the Beavers-Joseph-Saffman boundary condition still applies for oscillatory flows, provided the frequency of oscillation is not too high.
Abstract: We determine the hydrodynamics of a rigid, weakly permeable sphere undergoing translational oscillations in an incompressible Newtonian fluid. We check using homogenization and scaling arguments that the flow inside the sphere may be modeled by Darcy’s law and that the Beavers–Joseph–Saffman (BJS) boundary condition still applies for oscillatory flows, provided the frequency of oscillation is not too high. The BJS boundary condition introduces a slip velocity and to leading order in e=k/a, where k is the particle permeability and a is the radius, the particle may be regarded as impermeable with a slip length independent of frequency. Under these circumstances we solve for the flow field, pressure distribution and drag explicitly and show their behavior for 0⩽e⩽0.05 and frequencies relevant to electroacoustics (1–10 MHz). From the drag we find the leading order corrections due to particle permeability of the pseudo-steady drag, Basset force and added mass.

Journal ArticleDOI
TL;DR: In this paper, a multilevel representation of Daubechies compactly supported wavelet has been used to study the free vibrations of elastic catenary cables carrying an attached mass.

01 Nov 2004
TL;DR: In this article, the authors investigate the dynamics of a freely rising and falling cylinder and 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.
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.

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional rectangular profile is considered with the under-bottom clearance assumed to be small compared with structure dimensions and the water depth, and closed asymptotic formulae are obtained for all hydrodynamic coefficients for heave, sway and roll motions.

Journal ArticleDOI
TL;DR: In this paper, a methodology for detecting added mass in structural systems maintaining a linear response is presented, which uses a single frequency response function measured at several frequencies along with a correlated analytical model of the structure in its original state to detect and quantify the added mass.
Abstract: A methodology is presented for detecting added mass in structural systems maintaining a linear response. A single frequency response function measured at several frequencies along with a correlated analytical model of the structure in its original state are used to detect and quantify the added mass. A computationally efficient method of recalculating a single frequency response function is utilized in the identification algorithm. Experimental results from a frame structure are presented to validate and assess the proposed approach.

Journal ArticleDOI
TL;DR: In this paper, the effects of a concentrated mass on chaotic oscillations of a shallow cylindrical shell under gravity and periodic acceleration were investigated, and the Galerkin method was used to calculate the chaotic response.

Journal ArticleDOI
TL;DR: In this paper, a numerical application algorithm for applying the CFAM matrix for a core seismic analysis is developed and applied to the 7-ducts core system to investigate the fluid effects on the dynamic characteristics and the seismic time history responses.
Abstract: In this paper, a numerical application algorithm for applying the CFAM (Consistent Fluid Added Mass) matrix for a core seismic analysis is developed and applied to the 7-ducts core system to investigate the fluid effects on the dynamic characteristics and the seismic time history responses. To this end, three cases such as the in-air condition, the in-water condition without the fluid coupling terms, and the in-water condition with the fluid coupling terms are considered in this paper. From modal analysis, the core duct assemblies revealed strongly coupled out-of-phase vibration modes unlike the other cases with the fluid coupling terms considered. From the results of the seismic time history analysis, it was also verified that the fluid coupling terms in the CFAM matrix can significantly affect the impact responses and the seismic displacement responses of the ducts.


01 Jan 2004
TL;DR: In this paper, an improved Volume Of Fluid (iVOF) method is presented for the better numerical prediction of the behavior of a sub-sea structure in the splash zone.
Abstract: Existing simulation methods are not able to determine in detail the wave loads on a complex sub-sea structure when it is passing through the splash zone. To determine these loads, model tests are necessary. Otherwise only simplified formulations or empirical relations for added mass and damping can be used. The improved Volume Of Fluid (iVOF) method presented in this paper is a potential candidate for the better numerical prediction of the behaviour of a sub-sea structure in the splash zone. The simulated flow around and through the structure looks very realistic and shows a strong resemblance with observations from model tests. The quantitative comparison of the vertical load on the sub-sea structure shows that the total load levels are well predicted. This good initial comparison shows the potential of the iVOF method for the simulation of the behaviour of sub-sea structures in the splash zone. However, significant further development and validation is needed before a fully coupled simulation of a sub-sea structure and its lifting vessel in waves can be carried out. This possibility is also affected by the long simulation times required at the moment. As an intermediate step the method might be used to determine the wave loads and added mass in an uncoupled simulation.