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Charles H. K. Williamson - One of the best experts on this subject based on the ideXlab platform.

  • Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled Damping
    Journal of Fluid Mechanics, 2006
    Co-Authors: Raghuraman N Govardhan, Charles H. K. Williamson
    Abstract:

    In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural Damping, enabling the system to take on both negative and positive Damping. This permits a systematic study of the effects of system Mass and Damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of Mass–Damping ($\alpha$), in the so-called ‘Griffin plot’.

  • MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW Mass-Damping
    Journal of Fluids and Structures, 1999
    Co-Authors: Asif Khalak, Charles H. K. Williamson
    Abstract:

    These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low Mass and Damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined Mass-Damping parameter (low m*ζ), or a high Mass-Damping (highm*ζ ). For our low m*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the Mass-Damping (m*ζ), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the Mass ratio, m*ζ. At low (m*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of Mass ratios (m*=1–20), when plotted against (m*+CA) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m*+CA)ζ ∼0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m*+CA) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (fN), to form a normalized velocity (U*/f*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of Mass ratiosm* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*.

  • Investigation of relative effects of Mass and Damping in vortex-induced vibration of a circular cylinder
    Journal of Wind Engineering and Industrial Aerodynamics, 1997
    Co-Authors: Asif Khalak, Charles H. K. Williamson
    Abstract:

    Abstract An experimental study of vortex-induced vibration of a circular cylinder was conducted in a unique experimental facility especially designed for low Mass and low Damping. In this low Mass-Damping regime, two separate regions of the high amplitude response curve were identified, which we label “upper” and “lower” branches of response. A systematic study including twelve responses was performed to determine the effect of separately varying the nondimensional Mass and varying the nondimensional Damping. It seems apparent over the range of our present investigation that the Mass - Damping (the product of Mass and Damping) collapses well the amplitude of response, indicating two distinct amplitude curves, rather than the single, unique relationship previously supposed.

  • dynamics of a hydroelastic cylinder with very low Mass and Damping
    Journal of Fluids and Structures, 1996
    Co-Authors: Asif Khalak, Charles H. K. Williamson
    Abstract:

    Abstract An experimental facility for the study of the forces and response associated with vortex-induced vibration of a rigid cylinder has been constructed with extraordinarily low normalized Mass and normalized Damping. This facility achieves a level of combined Mass and Damping which is an order of magnitude less than previous studies of this type. Measurements of the total integrated forces on a static cylinder demonstrate the importance of the end conditions. By varying the end conditions, the case of vortices shed parallel to the cylinder was compared to the oblique shedding case. The results show that the mean drag is consistently higher in the parallel shedding case, throughout our range of Reynolds number, whereas the variation in r.m.s. lift is highly dependent on Reynolds number. At Re=12 000, the parallel case had five times the r.m.s. lift of the oblique case, a ratio which would become larger as the aspect ratio of the cylinder increases. However, despite this dependence upon Reynolds number in the magnitude of the lift force, the dominant nondimensional frequencies of the lift force were independent of Reynolds number, even in the present case of cellular shedding. Our study of the response in the hydroelastic case has brought two previously neglected points to the fore. Our data at very low Mass-Damping ratio shows that the response has two branches of resonance. The implication at low Mass-Damping ratios is that there are actually two distinct levels of resonance, rather than a single one as previously assumed. The second observation is that the adjustment of the Mass ratio affects the response, even when the combined Mass-Damping ratio is kept constant. An equation of motion is developed here, with inclusion of the inviscid “added-Mass” force which will necessarily become important at low Mass ratios.

Asif Khalak - One of the best experts on this subject based on the ideXlab platform.

  • MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW Mass-Damping
    Journal of Fluids and Structures, 1999
    Co-Authors: Asif Khalak, Charles H. K. Williamson
    Abstract:

    These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low Mass and Damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined Mass-Damping parameter (low m*ζ), or a high Mass-Damping (highm*ζ ). For our low m*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the Mass-Damping (m*ζ), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the Mass ratio, m*ζ. At low (m*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of Mass ratios (m*=1–20), when plotted against (m*+CA) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m*+CA)ζ ∼0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m*+CA) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (fN), to form a normalized velocity (U*/f*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of Mass ratiosm* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*.

  • Investigation of relative effects of Mass and Damping in vortex-induced vibration of a circular cylinder
    Journal of Wind Engineering and Industrial Aerodynamics, 1997
    Co-Authors: Asif Khalak, Charles H. K. Williamson
    Abstract:

    Abstract An experimental study of vortex-induced vibration of a circular cylinder was conducted in a unique experimental facility especially designed for low Mass and low Damping. In this low Mass-Damping regime, two separate regions of the high amplitude response curve were identified, which we label “upper” and “lower” branches of response. A systematic study including twelve responses was performed to determine the effect of separately varying the nondimensional Mass and varying the nondimensional Damping. It seems apparent over the range of our present investigation that the Mass - Damping (the product of Mass and Damping) collapses well the amplitude of response, indicating two distinct amplitude curves, rather than the single, unique relationship previously supposed.

  • dynamics of a hydroelastic cylinder with very low Mass and Damping
    Journal of Fluids and Structures, 1996
    Co-Authors: Asif Khalak, Charles H. K. Williamson
    Abstract:

    Abstract An experimental facility for the study of the forces and response associated with vortex-induced vibration of a rigid cylinder has been constructed with extraordinarily low normalized Mass and normalized Damping. This facility achieves a level of combined Mass and Damping which is an order of magnitude less than previous studies of this type. Measurements of the total integrated forces on a static cylinder demonstrate the importance of the end conditions. By varying the end conditions, the case of vortices shed parallel to the cylinder was compared to the oblique shedding case. The results show that the mean drag is consistently higher in the parallel shedding case, throughout our range of Reynolds number, whereas the variation in r.m.s. lift is highly dependent on Reynolds number. At Re=12 000, the parallel case had five times the r.m.s. lift of the oblique case, a ratio which would become larger as the aspect ratio of the cylinder increases. However, despite this dependence upon Reynolds number in the magnitude of the lift force, the dominant nondimensional frequencies of the lift force were independent of Reynolds number, even in the present case of cellular shedding. Our study of the response in the hydroelastic case has brought two previously neglected points to the fore. Our data at very low Mass-Damping ratio shows that the response has two branches of resonance. The implication at low Mass-Damping ratios is that there are actually two distinct levels of resonance, rather than a single one as previously assumed. The second observation is that the adjustment of the Mass ratio affects the response, even when the combined Mass-Damping ratio is kept constant. An equation of motion is developed here, with inclusion of the inviscid “added-Mass” force which will necessarily become important at low Mass ratios.

Mohammed Jameel - One of the best experts on this subject based on the ideXlab platform.

  • numerical investigation of the vortex induced vibration of an elastically mounted circular cylinder at high reynolds number re 104 and low Mass ratio using the rans code
    PLOS ONE, 2017
    Co-Authors: Niaz B Khan, Zainah Ibrahim, Muhammad Faisal Javed, Mohammed Jameel
    Abstract:

    This study numerically investigates the vortex-induced vibration (VIV) of an elastically mounted rigid cylinder by using Reynolds-averaged Navier–Stokes (RANS) equations with computational fluid dynamic (CFD) tools. CFD analysis is performed for a fixed-cylinder case with Reynolds number (Re) = 104 and for a cylinder that is free to oscillate in the transverse direction and possesses a low Mass-Damping ratio and Re = 104. Previously, similar studies have been performed with 3-dimensional and comparatively expensive turbulent models. In the current study, the capability and accuracy of the RANS model are validated, and the results of this model are compared with those of detached eddy simulation, direct numerical simulation, and large eddy simulation models. All three response branches and the maximum amplitude are well captured. The 2-dimensional case with the RANS shear–stress transport k-w model, which involves minimal computational cost, is reliable and appropriate for analyzing the characteristics of VIV.

  • stochastic response of intact and a removed tendon tension leg platform to random wave and current forces
    Arabian Journal for Science and Engineering, 2017
    Co-Authors: D. O. Oyejobi, Mohammed Jameel, Nor Hafizah Ramli Sulong
    Abstract:

    This work analysed the dynamic response of intact and a removed tendon tension leg platform (TLP) in simultaneous action of random wave and current loads in normal and less severe environments. Two different sea states of extreme severe sea state but less probable and less severe state and most probable are considered in this study. The artificial random wave is simulated by Monte Carlo simulation using Pierson–Moskowitz spectrum. Wave diffraction effect is not considered since the ratio of characteristic dimension to wavelength is less than limit. The coupling in all degree of freedoms and various degrees of nonlinear effects is considered. The inertia, Mass, Damping matrices of equation of motion and hydrodynamic force vector are formulated and solved numerically using Newmark integration scheme. The statistical results show that removal of one tendon increases surge and tendon tension values, while heave and pitch are not adversely affected in both environments. The response values of the TLP in extreme severe sea state are quite higher compared to less severe sea state. The percentage increase in all degree of freedoms and tendon tension is <5 % when one tendon is removed as compared to intact tendon TLP. It could be concluded that maximum and minimum tension in tendon constraints is equally passed by the TLP tendons.

Shi, Mendeley Z Data) - One of the best experts on this subject based on the ideXlab platform.

  • Analytical solutions to VBI system (simply supported boundary condition) considering both vehicle and bridge Damping effects and multiple bridge vibration modes
    2020
    Co-Authors: Shi, Mendeley Z Data)
    Abstract:

    Matlab codes developed to calculate vehicle and bridge responses (displacement, velocity, and acceleration) for a theoretical vehicle bridge interaction (VBI) system (simply supported boundary condition) reestablished to consider both the vehicle and bridge Damping effects and multiple bridge vibration modes. Hypothesis: Multiple bridge dynamic information may be extracted from the vehicle that travels on it. Assumption: 1. The magnitude of the vehicle acceleration signal (gravitational direction) is negligible compared to the gravitational acceleration constant (g), say 20%; 2. Uniformly distributed bridge property (Mass, Damping, section stiffness); 3. Vehicle traveling speed is constant. Limit: 1. The bridge is considered as the Bernoulli-Euler beam, flexure effects caused by shear forces, rotary inertial forces, and axial forces are not considered; 2. For zero initial conditions of bridge and vehicle only; 3. Other flaws may also apply

  • Analytical solutions to VBI system (simply supported boundary condition) considering both vehicle and bridge Damping effects and multiple bridge vibration modes
    2020
    Co-Authors: Shi, Mendeley Z Data)
    Abstract:

    Matlab codes developed to calculate vehicle and bridge responses (displacement, velocity, and acceleration) for a theoretical vehicle bridge interaction (VBI) system (simply supported boundary condition) reestablished to consider both the vehicle and bridge Damping effects and multiple bridge vibration modes. Hypothesis: Multiple bridge dynamic information may be extracted from the vehicle that travels on it. Assumption: 1. The magnitude of the vehicle acceleration signal (gravitational direction) is negligible compared to the gravitational acceleration constant (g), say 20%; 2. Uniformly distributed bridge property (Mass, Damping, section stiffness); 3. Vehicle traveling speed is constant. Limit: 1. The bridge is considered as the Bernoulli-Euler beam, flexure effects caused by shear forces, rotary inertial forces, and axial forces are not considered; 2. For zero initial conditions of bridge and vehicle only; 3. Other flaws may also apply. Note: Two forms of solutions are presented for cross-checking purposes, choose either SSB_dvb.m or SSB_dvb_check.m, the results for vehicle and bridge should be the same, but allow for minor differences due to truncations of numerical calculation

  • Analytical solutions to VBI system for non-simply supported boundary conditions
    2020
    Co-Authors: Shi, Mendeley Z Data)
    Abstract:

    Matlab codes developed to calculate vehicle and bridge responses (displacement, velocity, and acceleration) for a theoretical vehicle bridge interaction (VBI) system for non-simply supported boundary conditions including both ends fixed, fixed simply supported, and one end fixed the other end free (cantilever) boundary condition. Both the vehicle and bridge Damping effects and multiple bridge vibration modes are considered. Hypothesis: Multiple bridge dynamic information may be extracted from the vehicle that travels on it. Assumption: 1. The magnitude of the vehicle acceleration signal (gravitational direction) is negligible compared to the gravitational acceleration constant (g), say 20%; 2. Uniformly distributed bridge property (Mass, Damping, section stiffness); 3. Vehicle travelling speed is constant. Limit: 1. Based on Bernoulli-Euler beam theory, flexure effects caused by shear forces, rotary inertial forces, and axial forces are not considered; 2. For zero initial conditions of bridge and vehicle only; 3. Other flaws may also apply, use with caution. Note: Two forms of solutions are presented for cross-checking purposes, the numerical results for vehicle and bridge are almost the same, only allow for minor differences due to truncation issue existed in numerical calculations

Mingjie Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a simplified model to evaluate peak amplitude for vertical vortex induced vibration of bridge decks
    International Journal of Mechanical Sciences, 2021
    Co-Authors: Mingjie Zhang
    Abstract:

    Abstract A simplified model is developed to conveniently evaluate the peak vortex-induced vibration (VIV) amplitudes of a bridge deck at various Mass-Damping conditions. As a simplified form of the describing function-based model previously developed by the authors, the key innovation of the new model is the introduction of an envelope curve of the aerodynamic describing functions (or amplitude-dependent flutter derivatives), which determines the maximum negative aerodynamic Damping versus vibration amplitude in the lock-in range. Based on the envelope curve, the peak VIV amplitudes at different Mass-Damping conditions can be obtained directly without calculating all the VIV amplitudes in the entire lock-in range. The new model is more practical for engineers in the bridge engineering community since it only contains a single group of aerodynamic parameters which don't vary with the reduced wind speed. The envelope curve can be either identified based on the VIV decay-to-resonance and/or grow-to-resonance signals at a single Mass-Damping condition, or based on the VIV steady amplitudes at different Mass-Damping conditions. Numerical examples involving the VIV analyses of a rigid rectangular cylinder and a bridge deck sectional model are utilized to validate the simulation accuracy of the proposed model, and the model is applied to calculate the peak VIV amplitudes of two flexible bridge decks at various mechanical Damping levels. The proposed model is capable of accurately and conveniently predicting the peak VIV amplitudes of a bridge deck sectional model at various Mass-Damping conditions. For a flexible bridge deck, the peak VIV amplitude calculated by the proposed model is slightly conservative due to the overestimated negative aerodynamic Damping at some span-wise segments of the bridge deck. The superiority of the proposed model relative to the conventional van der Pol-type model is also demonstrated.