Effects Of Viscous Damping Research Articles

Robust turbulence simulation for particle-based fluids using the Rankine vortex model

We propose a novel turbulence refinement method based on the Rankine vortex model for smoothed particle hydrodynamics (SPH) simulations. Surface details are enhanced by recovering the energy lost due to the lack of the rotation of SPH particles. The Rankine vortex model is used to convert the diffused and stretched angular kinetic energy of particles to the linear kinetic energy of their neighbors. In previous vorticity-based refinement methods, adding more energy than required by the viscous damping effect leads to instability. In contrast, our model naturally prevents the positive feedback effect between the velocity and vorticity fields since the vortex model is designed to alter the velocity without introducing external sources. Experimental results show that our method can recover missing high-frequency details realistically and maintain convergence in both static and highly dynamic scenarios.

On effects of viscous damping of harmonically varying axially moving string

On effects of viscous damping of harmonically varying axially moving string

Maximization of wave power extraction of a heave point absorber with a sea-state-based causal control algorithm

A causal control strategy is developed to tackle the non-causality arising in the real-time implementation of optimal wave energy control. The proposed control strategy utilizes a causal approximation transfer function to link the current wave force to the desired buoy velocity so as to eliminate the non-causality. An optimum model of the approximation transfer function is derived considering the power density distribution of the local wave spectrum. Based on the optimized approximation transfer function, the desired buoy velocity is achieved by tuning the power take-off mechanical force with the PID control. The efficiency of the proposed causal control strategy is assessed for a heaving point-absorber, in a set of random wave conditions. Generally, the heaving point-absorber could extract wave power up to 90% of the theoretical upper bound using the proposed control strategy. The sensitivity of the proposed control to viscous damping effect due to drag and wave spectrum bandwidth is investigated. Although it is less efficient in broad-banded sea state, the control efficiency is still within an acceptable level (above 70%).

Investigating the viscous damping effects on the propagation of Rayleigh waves in a three-layered inhomogeneous plate

The present paper investigates the propagation of anti-plane Rayleigh waves in an elastic three-layered inhomogeneous plate in the presence of viscous damping. The core layer is sandwiched between skin layers with appropriate perfect interfacial boundary conditions, while traction-free conditions are prescribed on the outer faces. The eigenfunctions expansion method is employed for the study. Various cases of damped and undamped situations have been examined in connection to the obtained displacements and shear stresses. Finally, the effects of viscous damping on the propagation of Rayleigh waves are reported graphically using some physical available data.

Exploring inelastic collisions using modified three-dimensional discontinuous deformation analysis incorporating a damped contact model

Abstract Most collisions in reality are partially inelastic. The consideration of energy dissipation is important in block collision phenomena. Therefore, damping should be introduced into three-dimensional discontinuous deformation analysis (3D DDA) to address the energy loss in collisions. A damped contact model based on linear spring-dashpot assumption is adopted and incorporated into 3D DDA. The derivation is first presented to obtain the formulae of the damped contact model in normal and shear directions, and then a single-degree-of-freedom example is modelled to validate the modified 3D DDA. Subsequently, inelastic collisions with unconstrained and fixed targets are carefully investigated. A relationship between viscous damping coefficient and coefficient of restitution (COR) is derived. Finally, viscous damping effect in contact is demonstrated by a freefall example of an assembly of blocks. The results suggest that the modified 3D DDA can model the collision behavior under given COR, and the damping effect may be significant and should be properly addressed in simulations.

Fluid Dynamics of Ballistic Strategies in Nematocyst Firing

Nematocysts are stinging organelles used by members of the phylum Cnidaria (e.g., jellyfish, anemones, hydrozoans) for a variety of important functions including capturing prey and defense. Nematocysts are the fastest-known accelerating structures in the animal world. The small scale (microns) coupled with rapid acceleration (in excess of 5 million g) present significant challenges in imaging that prevent detailed descriptions of their kinematics. The immersed boundary method was used to numerically simulate the dynamics of a barb-like structure accelerating a short distance across Reynolds numbers ranging from 0.9–900 towards a passive elastic target in two dimensions. Results indicate that acceleration followed by coasting at lower Reynolds numbers is not sufficient for a nematocyst to reach its target. The nematocyst’s barb-like projectile requires high accelerations in order to transition to the inertial regime and overcome the viscous damping effects normally encountered at small cellular scales. The longer the barb is in the inertial regime, the higher the final velocity of the projectile when it touches its target. We find the size of the target prey does not dramatically affect the barb’s approach for large enough values of the Reynolds number, however longer barbs are able to accelerate a larger amount of surrounding fluid, which in turn allows the barb to remain in the inertial regime for a longer period of time. Since the final velocity is proportional to the force available for piercing the membrane of the prey, high accelerations that allow the system to persist in the inertial regime have implications for the nematocyst’s ability to puncture surfaces such as cellular membranes or even crustacean cuticle.

Modeling blood flow in viscoelastic vessels: the 1D augmented fluid–structure interaction system

Nowadays mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes in different medical sectors. The theory behind blood flow modeling is closely related to the study of incompressible flow through compliant thin-walled tubes, starting from the incompressible Navier–Stokes equations. Furthermore, the mechanical interaction between blood flow and vessels wall must be properly described by the model. Recent works showed the benefits of characterizing the rheology of the vessel wall through a viscoelastic law. Taking into account the viscous contribution of the wall material and not simply the elastic one leads to a more realistic representation of the vessel behavior, which manifests not only an instantaneous elastic strain but also a viscous damping effect on pulse pressure waves, coupled to energy losses. In this context, the aim of this work is to propose an easily extensible one-dimensional mathematical model able to accurately capture fluid–structure interactions. The originality of the model lies in the introduction of a viscoelastic tube law in PDE form, valid for both arterial and venous networks, leading to an augmented fluid–structure interaction system. In contrast to well established mathematical models, the proposed one is natively hyperbolic. The model is solved with an efficient and robust second-order numerical scheme; the time integration is based on an Implicit–Explicit Runge–Kutta scheme conceived for applications to hyperbolic systems with stiff relaxation terms. The validation of the proposed model is performed on several different test cases. Results obtained in Riemann problems, adopting a simple elastic tube law for the characterization of the vessel wall, are compared with available exact solutions. To validate the contribution given by the viscoelastic term, the Method of Manufactured Solutions has been applied. Specific tests have been designed to verify the well-balancing with respect to fluid-at-rest condition and the accuracy-preserving property of the scheme. Finally, a specific test case with an inlet pulse pressure wave has been designed to assess the effects of viscoelasticity with respect to a simple elastic behavior of the vessel wall. The complete code, written in MATLAB (MathWorks Inc.) language, with the implemented test cases, is made available in Mendeley Data repository.

Stability analysis of an axially moving nanocomposite circular cylindrical shell with time-dependent velocity in thermal environments

This article investigates the instability of an axially moving simply supported nanocomposite circular cylindrical shell reinforced by single-walled carbon nanotubes (SWCNTs) with time variant velocity in thermal environments considering the effect of viscous structure damping. The nanocomposite material properties are obtained from the extended mixture rule for uniformly distributed CNT, furthermore three different types of functionally graded distribution CNT in the matrix are represented. In addition, the Hamilton principle via the simplification assumption of the Donnell shallow-shell theory is employed to derive motion equations. At first, related displacements are obtained in terms of displacement in radius direction which is expressed in a combination of driven and companion modes from motion equations in axial and circumferential directions. The dimensionless motion equation in radius direction is discretized by the Galerkin method. The critical speed values of different types of CNT distribution reinforcement, various types of volume-fraction of CNT reinforcement and different temperatures are established using the multiple scale method. Moreover, the first order solution of the perturbation theory makes it possible to predict the unstable regions of principle parametric resonances and combination resonances. It occurs under the effect of temperature rising condition, changing the kind of SWCNTs as well as increasing the value of viscous structure damping, volume-fraction of CNT distribution, constant part of velocity function and fluctuation domain. Results show a system with the symmetric distribution of CNT reinforcement, while the outer and inner are CNT-rich, represents higher stability in axially moving nanocomposite cylindrical shells with constant and time-dependent velocity. Communicated by Eleonora Tubaldi

Experimental and numerical study of dynamic responses of a new combined TLP type floating wind turbine and a wave energy converter under operational conditions

This paper deals with a novel concept by combining a tension leg platform (TLP) type floating wind turbine and a heave-type wave energy converter, that is referred as the ‘TWWC’ (TLP-WT-WEC- Combination) system herein. Dynamic responses of the TWWC system under operational seas cases (in South China Sea) have been investigated by using both time-domain numerical simulation and scale model tests (1:50). For the numerical model, hydrodynamic loads of the TLP and the WEC are calculated by the AQWA code, which is available for modeling multi-body systems including both mechanical and hydrodynamic couplings between the TLP and the WEC. The aerodynamic loads of the wind turbine are calculated based on the NREL 5 MW wind turbine. The scale model tests have been done in Harbin Institute of Technology’s wind tunnel & wave flume joint laboratory. The power-take-off (PTO) system of the WEC device is simulated by two nonlinear air-dampers, and aerodynamic loads of the wind turbine are simulated by a scaled rotating wind turbine model with equivalent mean thrust effect. Main dynamic characteristics of the TWWC system under operational sea cases have been clarified. Numerical and experimental results are presented and compared. Good agreements are achieved, although the numerical model tends to overestimate dynamic responses of the TWWC system due to ignoring the viscous damping effect in the scale test model. The validated numerical model of the TWWC system will be useful for future optimal design of the WEC PTO system.

DEM verification of the damping effect in a freely falling particle motion for quasi- and non-quasi-static conditions

The discrete element method (DEM) has been widely used in numerical evaluations in geotechnical engineering; however, simple analysis and verification are still needed to obtain the interaction mechanism between a single particle and a wall under a damping effect. A single freely falling particle model is proposed, and the analytical solutions for the stages of particle freefall, fixed wall contact, and rebound are obtained for different damping types and values. Timestepping in quasi-static and non-quasi-static conditions is considered for better understanding of the DEM hypothesis. The numerical results are quite consistent with the analytical solution. The linear and exponential relationships between the restitution coefficient and the local and viscous damping, respectively, are obtained and formulized. Kinetic energy dissipation is larger with the viscous damping effect than for the local damping when comparing the particle rebound height. Verification of the analytical and numerical solutions has been conducted with the previous studies which shows good agreement. The timestep is no longer constant when the particle velocity exceeds approximately 1.55 m/s, which means the DEM system is no longer quasi-static.

Free vibration and stability of an axially moving thin circular cylindrical shell using multiple scales method

This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress–strain relation considering Hook’s Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell–Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction. As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.

Extension and application of Discontinuous Deformation Analysis with a damped contact spring model

Discontinuous Deformation Analysis (DDA) is widely used in geological and geotechnical engineering. To provide an alternative approach to considering damping effect in dynamic analysis, a damped contact spring model is implemented. The model assumes that the damping component – linear dashpot - takes place in joints of DDA models. The normal and shear damping forces are determined according to the relative velocities of the two contacted points. A semi-analytical solution is also proposed to calculate damping coefficient from a given damping ratio. The viscous damping effect produced by the damped contact spring model is independent to step size. The proposed model is incorporated into DDA program, and then several classic damping dynamic examples are constructed to validate the contact model, showing good agreement with analytical solutions. After that, a seismic spectrum of a recorded ground motion is analyzed to show the contact model is suitable for response spectrum generation. Finally, the Donghekou landslide case is studied under different parameters, suggesting that the proper consideration of damping is essential to natural hazard analysis.

Collapse-Limit Input Level of Critical Double Impulse for Damped Bilinear Hysteretic SDOF System With Negative Post-yield Stiffness

The collapse-limit input velocity level of the critical double impulse simulating the principal part of near-fault ground motions is derived for an elastic-plastic structure with viscous damping and P-delta effect. The structural system is modeled by a bilinear hysteretic SDOF system with negative post-yield stiffness reflecting the P-delta effect which plays a key role in the collapse behavior. Since the critical timing of the second impulse in the double impulse has been proven as the zero-restoring force timing after the first impulse for the elastic-plastic SDOF system with viscous damping, that property is used again in this paper. It is shown that the collapse-limit input level of the critical double impulse can be obtained as a function of the post-yield stiffness and the damping ratio by using the energy balance law and the quadratic-function approximation of the damping force-deformation relation. The applicability of the collapse-limit level to actual recorded ground motions is investigated through the time-history response analysis for the stable and collapse models under two actual earthquake ground motions.

Viscous damping effect and vortex shedding performance of the novel anti-motion structures on a cylindrical FPSO

In order to decrease the dynamic response of cylindrical FPSO, a novel anti-motion structures with taper angle is proposed. According to the computational fluid dynamics approach, the influence of different taper angles and pore diameters are numerically studied in present work. To investigate both viscous damping and vortex shedding performance of heave and pitch motions, dynamic mesh method and user defined functions are adopted. After a series of validation and convergence test works, the numerical models of the cylindrical FPSO with different taper anti-motion structure is established, and the damping coefficients are calculated via these models. Besides, the vortex shedding performance is documented by vorticity graphs. Results show that the heave damping coefficient decreases with the increasing taper angle. On the other hand, less pitch damping coefficients are found when the smaller pore diameter is adopted. An interesting finding is that pores on the anti-motion structure do benefit to increase the damping performance, but the diameter should not exceed a limit.

Deformation study of an in-plane oscillating dielectric elastomer actuator having complex modes

Due to the deformation ability over a wide frequency range, dielectric elastomer actuators (DEAs) under an alternating electric load have received increasing attention. In the theoretical analysis of an in-plane oscillating DEA (edge clamped membrane without a pressure load), the assumption of homogeneous deformation is applied, which conflicts with the observed non-uniform deformation under a combination of pressure and voltage load. To validate the simplification, experimental and theoretical studies of a circular DEA under alternating voltage are reported here. A laser Doppler vibrometer is used to acquire the full-field oscillating response of the DEA fabricated by commercial VHB4905 with hydrogel electrodes. The measured amplitude and phase illustrate that the assumption of homogeneous deformation only works at low frequencies, whereas the non-uniform deformation dominates the oscillation with the increase of excitation frequency. In addition, the in-plane oscillating DEA behaves as a complex mode system. Accordingly, the motion equation is proposed by considering the general viscous damping effect. The experimentally observed transition (from uniform to non-uniform deformation) is analyzed numerically. The normalized upper frequency, under which the deformation field can be treated as uniform, is also obtained based on full-wave simulations.

A Fully Differential SOI-MEMS Thermal Piezoresistive Ring Oscillator in Liquid Environment Intended for Mass Sensing

In this paper, we present a silicon on insulator (SOI)-based MEMS oscillator that comprises a ring-shaped rotational mode resonator incorporating fully differential design for operation in aquatic environment using the thermal drive piezoresistive sense transduction. The differential scheme used in the resonator design enables high feedthrough cancellation, thus leading to floor value close to −62 dB with sufficient signal to feedthrough ratio (SFR) and allowing a later oscillator implementation. The proposed differential ring-shaped thermal piezoresistive resonator (DR-TPR) when made to operate in the rotational mode exhibits the special feature of minimizing the effect of viscous damping in liquid environment, attaining a quality factor value as high as 537 with a stopband rejection of 8.5 dB. The closed-loop measurement using the HF2LI lock-in amplifier with PLL from Zurich Instruments helps us to realize the differential ring-shaped thermal piezoresistive oscillator (DR-TPO) showing phase noise of −77.6 dBc/Hz at 1-kHz offset and −89.54 dBc/Hz at 10-kHz offset. The proposed DR-TPO in liquid environment can provide a frequency resolution of 6.95 Hz extracted from the measured Allan deviation, which corresponds to a minimum detectable mass of 4.11 pg, thus paving a way to both physical and biomedical detection in liquid.

Nonlocal Effect on the Pull-in Instability Analysis of Graphene Sheet Nanobeam Actuator

ABSTRACTIn this study, the pull-in phenomenon of a Nano-actuator is investigated employing a nonlocal Bernoulli-Euler beam model with clamped-clamped conditions. The model accounts for viscous damping, residual stresses, the van der Waals (vdW) force and electrostatic forces with nonlocal effects. The hybrid differential transformation/finite difference method (HDTFDM) is used to analyze the nonlocal effects on a graphene sheet nanobeam, which is electrostatically actuated under the influence of the coupling effect, the von Kármán nonlinear strains and the fringing field effect. The pull-in voltage as calculated by the presented model deviates by no more than 0.29% from previous literature, verifying the validity of the HDTFDM. Furthermore, the nonlocal nonlinear behavior of the electrostatically actuated nanobeam is investigated, and the effects of viscous damping, residual stresses, and length-gap ratio are examined in detail. Overall, the results reveal that small scale effects significantly influence the characteristics of the graphene sheet nanobeam actuator.

Review of applications of self‐excited oscillations to highly sensitive vibrational sensors

AbstractVibrational sensors with resonators are suited for online monitoring because of their fast response and ability to measure instantly and continuously. Also, their miniaturization realizes much higher resolution. In this review, we begin by discussing sensor resolution based on the natural frequency shift of the resonator. For mass and stiffness sensing, the detection method for the natural frequency shift by self‐excited oscillation is characterized comparing with that by external excitation. Self‐excited oscillation automatically compensates for the viscous damping effects of the environment on the resonators, thus ensuring direct and accurate detection of the natural frequency shift. Another application of self‐excited oscillation is to viscometers. Instead of detecting the natural frequency shift, this system detects the critical feedback gain to generate self‐excited oscillation. This is important for measuring very high viscosity, where the peak of the frequency response curve is ambiguous or does not exist, meaning the Q value cannot be estimated from such curves. Another method, introduced for ultra‐sensitive mass sensing, is based on the eigenmode shift in multiple weakly coupled resonators. In this system, the self‐excitation compensates for the viscous damping effects to enable direct detection of the eigenmode shift.

A numerical and experimental investigation of the effect of side walls on hydrodynamic model testing in a wave flume

The side wall effect was normally tackled by potential flow based numerical methods. It is well known that, due to the existence of the resonance frequency in the wave tank, the numerical methods over-predict the hydrodynamic forces when comparing with model experiments. Furthermore, in most of the previous studies on the effects of the side walls, the model was located at the centre of the tank, the disturbances on both sides of the model are symmetric, and the resonances of some of the responses such as wave surface elevation and motions may not be excited at the tank natural frequencies. In the present study, a Rankine source panel method is used to tackle the effects of the side walls and artificial damping is introduced in the free surface boundary condition to account for the viscous damping effect. Model experiments are carried out for a lifeboat model located at various positions in a wave flume. Numerical results of the wave forces, free surface elevations and motions of the model are compared with the model test measurements, and good agreement is found. It is shown that the inclusion of the artificial damping in the free surface boundary condition is effective, in particular for the model at off-centre position of the tank.

Experimental modal analysis of disk-like rotor–stator system coupled by viscous liquid

The vibrational behavior of a rotor–stator system coupled by a viscous liquid is investigated experimentally using a test bench with rotor and stator simplified as disks. The understanding of this vibration problem is of particular importance in the design of hydraulic machines such as Francis turbines, pump–turbines or hydraulic pumps, where the elastic rotor is coupled to the adjacent elastic stator by the intermediate water. The especially developed test bench enables high-resolution scan measurements of the rotor and stator disk vibrations by applying the modal analysis method in combination with the laser interferometer technique. We present the mode shapes, eigenfrequencies and damping factors measured over a large number of parameter combinations of the stator thickness, the rotor thickness, the clearance between rotor and stator as well as the rotation speed of the rotor. We identify and discuss fundamental vibration mechanisms of the system (for example, the characterization of varicose and sinuous modes, or the frequency split between co- and counter-rotating modes). The derived experimental results may serve as a benchmark for the validation of simulation models studying the linear vibration including effects of rotation, bias flow and viscous damping.