Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

A Provable Positivity-Preserving Local Discontinuous Galerkin Method for the Viscous and Resistive MHD Equations

In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

Application of computational fluid dynamics in design of viscous dampers-CFD modeling and full-scale dynamic testing

Computational fluid dynamics(CFD)provides a powerful tool for investigating complicated fluid flows.This paper aims to study the applicability of CFD in the preliminary design of linear and nonlinear fluid viscous dampers.Two fluid viscous dampers were designed based on CFD models.The first device was a linear viscous damper with straight orifices.The second was a nonlinear viscous damper containing a one-way pressure-responsive valve inside its orifices.Both dampers were detailed based on CFD simulations,and their internal fluid flows were investigated.Full-scale specimens of both dampers were manufactured and tested under dynamic loads.According to the tests results,both dampers demonstrate stable cyclic behaviors,and as expected,the nonlinear damper generally tends to dissipate more energy compared to its linear counterpart.Good compatibility was achieved between the experimentally measured damper force-velocity curves and those estimated from CFD analyses.Using a thermography camera,a rise in temperature of the dampers was measured during the tests.It was found that output force of the manufactured devices was virtually independent of temperature even during long duration loadings.Accordingly,temperature dependence can be ignored in CFD models,because a reliable temperature compensator mechanism was used(or intended to be used)by the damper manufacturer.

Influence of viscous force on the dynamic process of micro-sphere in optical tweezers

With the advantages of noncontact,high accuracy,and high flexibility,optical tweezers hold huge potential for micro-manipulation and force measurement.However,the majority of previous research focused on the state of the motion of particles in the optical trap,but paid little attention to the early dynamic process between the initial state of the particles and the optical trap.Note that the viscous forces can greatly affect the motion of micro-spheres.In this paper,based on the equations of Newtonian mechanics,we investigate the dynamics of laser-trapped micro-spheres in the surrounding environment with different viscosity coefficients.Through the calculations,over time the particle trajectory clearly reveals the subtle details of the optical capture process,including acceleration,deceleration,turning,and reciprocating oscillation.The time to equilibrium mainly depends on the corresponding damping coefficient of the surrounding environment and the oscillation frequency of the optical tweezers.These studies are essential for understanding various mechanisms to engineer the mechanical motion behavior of molecules or microparticles in liquid or air.

Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

Heat Propagation of Eyring-Prandtl Double Reaction and Pressure Driven Hydromagnetic Viscous Heating Fluid in a Device

The effect toxic industrial discharge on the environment and ecosystem cannot be overlooked. This is owing to a partial combustion of hydrocarbon arising from industrial activities and human endeavours. As such, this investigation focuses on the pressure driven flow and heat propagation of combustible Prandtl-Eyring viscous heating fluid in a horizontal device. The combustion-reaction of the viscoplastic material is considered to be inspired by two-step exothermic reaction. With negligible reactant consumption, the flowing fluid is influenced by a chemical kinetic, activation energy and electromagnetic force. An invariant transformation of the partial derivative model to an ordinary derivative model is obtained through an applied dimensionless variable. The solutions to the unsteady thermal fluid flow model are obtained via a semi-implicit difference scheme, and the outputs of the solution are displayed in plots and tables. As revealed, an enhanced heat propagation is obtained that in turn encourages the combustion process of the system. Also, increasing material dilatant simulated fluid molecular bond and viscosity. Therefore, the outcomes of this study are treasured to the thermal and chemical engineering, and the environmental management.

Geometrical Evaluation on the Viscous Effect of Point-Absorber Wave-Energy Converters

The fluid viscosity is known to have a significant effect on the hydrodynamic characteristics which are linked to the power conversion ability of the wave energy converter(WEC). To overcome the disadvantages of case-by-case study through the experiments and numerical computations employed by the former researches, the viscous effect is studied comprehensively for multiple geometries in the present paper. The viscous effect is expressed as the viscous added mass and damping solved by the free-decay method. The computational fluid dynamics(CFD) method is employed for the calculation of the motion and flow field around the floater. The diameter to draft ratio and bottom shape are considered for the geometrical evaluation on the viscous effect. The results show that a slenderer floater presents a stronger viscous effect. Through the comparisons of the floaters with four different bottom shapes, the conical bottom is recommended in terms of low viscous effect and simple geometry for manufacture. A viscous correction formula for a series of cylindrical floaters is put forward, for the first time, to help the engineering design of outer-floaters of point-absorber WECs.

Loss of energy dissipation capacity from the deadzone in linear and nonlinear viscous damping devices

In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper＇s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of ＂deadzone＂. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect ofdeadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 3 5 6 for calculation of equivalent damping if a deadzone is to be considered.

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Viscous Fluid Flowing around the Plate: Turbulence

Diffusion of momentum gives rise to viscosity. This article presents a solution in the explicit form of the equation of the momentum diffusion for a viscous fluid flowing around a plate taking into account deceleration. Three characteristic regions of a viscous flow have been described: the mantle, the body of the boundary layer, the viscous sublayer. In the mantle, the effect of viscosity is significant at a considerable distance from the plate. The momentum diffusion is focused in the body of the boundary layer. The diffusion force that produces the momentum of force giving rise to eddies is localized in the viscous sublayer. At the beginning of the plate, a moment of force twists the liquid along the flow, creating eddies that roll along the plate. For this reason, they are pressed against the surface of the plate. But at some distance from the beginning of the plate, the moment of force changes its orientation to the opposite and twists the vortices in the opposite direction, causing the vortices to roll along the plate against the flow. This causes the liquid to detach from the surface of the plate. This is the beginning of turbulence. The diameter of the vortex produced in the viscous sublayer is small being of the order of the thickness of the viscous sublayer. The vortex possesses a large angular velocity. Due to the momentum diffusion and the effect of the eddies combined in passing along the plate, its diameter increases up to the size of the thickness of the boundary layer and even more, whereas its angular velocity decreases down to the values really observed. The value of the critical Reynolds number of the transition from the laminar flow to the turbulent one has been found, and it agrees with the experimental data. The value of the shear stress produced by the viscous fluid on the plate surface has also been obtained. The way of measurement of the friction coefficient characterizing the effect of the plate on the flow has been proposed. It has been shown that the boundary condition of adhesion to the surface of a body flown around, that is applied in the estimation of viscous flows, contradicts the real processes of the flow.

Efficiency of the motion amplification device with viscous dampers and its application in high-rise buildings

After nearly a decade of application and investigation, a motion amplification device with viscous dampers for energy dissipation has been recognized as an effective solution to mitigate wind or seismic excitation, especially for stiff structural systems. As a result of compensation of amplified motion, it has been proved that the efficiency of viscous damper largely depends on the motion amplification device configuration, particularly for device stiflhess. In this paper, a ＂scissor-jack＂ type of motion amplification device, called a ＂toggle brace damper＂ system, is studied. It is demonstrated that the efficiency of such a device reflected by its amplification factor is not merely a function of its geometric configuration, but is highly dependent on the support elements＇ stiffness as well, similar to the mechanism of a leverage arm. Accordingly, a mathematical model in terms of complex modulus of the viscous damper with consideration of the support brace＇s stiffness is established. The results indicate that the efficiency of the motion amplification device with viscous dampers significantly depends on the stiffness of the support elements. Other parameters, such as toggle brace configuration and damping values of the viscous damper, are studied and compared. As an application example, numerical analyses are conducted to study the dynamic performance of a 39-story office tower installed with toggle brace dampers constructed on soft soil in a reclaimed area, under a combined effect of the vortex shedding of an adjacent existing 52-story building and earthquakes. The results show that viscous dampers with a motion amplification system using a properly designed toggle brace device proved to be an effective solution to alleviate the external excitations.

Finite element analysis of stiffness and static dent resistance of aluminum alloy double-curved panel in viscous pressure forming

The static dent resistance performance of the aluminum alloy double-curved panel formed using viscous pressure forming (VPF)was studied by finite element analysis,which mainly considers the forming process conditions.The whole simulation consisting of three stages,i.e.,forming,spring-back and static dent resistance,was carried out continuously using the finite element code ANSYS.The influence of blank holder pressure(BHP)and the drawbead on the stiffness and the static dent resistance of the panels formed using VPF was analyzed.The results show that the adequate setting of the drawbead can increase the plastic deformation of the double-curved panel,which is beneficial to the initial stiffness and the static dent resistance.There is an optimum BHP range for the stiffness and the static dent resistance.

Hybrid algorithm for modeling of fluid-structure interaction in incompressible, viscous flows

The objective of this paper is to present and to validate a new hybrid coupling （HC） algorithm for modeling of fluid-structure interaction （FSI） in incompressible, viscous flows. The HC algorithm is able to avoid numerical instability issues associated with artificial added mass effects, which are often encountered by standard loosely coupled （LC） and tightly coupled （TC） algorithms, when modeling the FSI response of flexible structures in incompressible flow. The artificial added mass effect is caused by the lag in exchange of interfacial displacements and forces between the fluid and solid solvers in partitioned algorithms. The artificial added mass effect is much more prominent for light/flexible struc- tures moving in water, because the fluid forces are in the same order of magnitude as the solid forces, and because the speed at which numerical errors propagate in an incom- pressible fluid. The new HC algorithm avoids numerical instability issues associated with artificial added mass effects by embedding Theodorsen＇s analytical approximation of the hydroelastic forces in the solution process to obtain better initial estimates of the displacements. Details of the new HC algorithm are presented. Numerical validation studies are shown for the forced pitching response of a steel and a plastic hydrofoil. The results show that the HC algorithm is able to converge faster, and is able to avoid numerical insta- bility issues, compared to standard LC and TC algorithms, when modeling the transient FSI response of a plastic hydrofoil. Although the HC algorithm is only demonstrated for a NACA0009 hydrofoil subject to pure pitching motion, the method can be easily extended to model general 3-D FSI response and stability of complex, flexible structures in turbulent, incompressible, multiphase flows.

Numerical Simulation of Viscous Flow Around a Rolling Cylinder with Ship-Like Section

Two-dimensional unsteady incompressible viscous flow around a rolling cylinder with ship-like section is numerically simulated by employing the computational scheme previously developed by the authors, in which the continuity and momentum equations are satisfied simultaneously at each time step for oscillating flow. The numerical results show that the motion of vortices around a rolling ship hull is cyclical. It is found that the location of the vortices is very similar to the existing experimental result. Using these simulation results, we can calculate the roll damping of ships including viscous effects.

Viscous-Flow-Based Analysis of Wave Near-Trapped in a Four-Cylinder Structure

The hydrodynamic analysis of multi-floating bodies is important and widely used in marine engineering. In this study, we systematically simulated the wave diffraction problem of a fixed vertical four-cylinder structure in regular waves in the time domain in a viscous numerical wave tank. The hydrodynamic interaction of waves with a bottom-mounted structure consisting of four vertical cylinders arranged at the corners of a square shows a complicated interference phenomenon. In this paper, we illustrate and analyze the run-up around the structure and the corresponding wave forces. To investigate the viscous effect on the near-trapping phenomenon, we pay particular attention to investigating the waves near-trapped inside the four-cylinder structure,and make a comparative study of the viscous-and inviscid-flow solutions with the experimental measurements. The results show that the maximum wave elevation occurs on the inner side of the leeside cylinder, and that the wave elevations on the outer side of the cylinders are lower than those on the inner side. We can conclude that viscosity has an obvious damping effect on wave elevations inside the structure. The cylinders show a tendency to drift apart from each other when the near-trapping phenomenon occurs.

PROPAGATION OF LOVE WAVES IN PRESTRESSED PIEZOELECTRIC LAYERED STRUCTURES LOADED WITH VISCOUS LIQUID

We investigate analytically the effect of initial stress in piezoelectric layered structures loaded with viscous liquid on the dispersive and attenuated characteristics of Love waves, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of initial stress in the piezoelectric layer and the viscous coefficient of the liquid on the phase velocity of Love waves are analyzed. Numerical results are presented and discussed. The analytical method and the results can be useful for the design of chemical and biosensing liquid sensors.

STABILITY OF VISCOUS CONTACT WAVE FOR COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS WITH FREE BOUNDARY

In this paper, we study the large time behavior of solutions to the nonisentropic Navier-Stokes equations of general gas, where polytropic gas is included as a special case, with a free boundary. First we construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation, in finite time as the heat conductivity tends to zero. Then we prove the viscous contact wave is asymptotic stable if the initial perturbations and the strength of the contact wave are small. This generalizes our previous result [6] which is only for polytropic gas.

Planar Velocity Distribution of Viscous Debris Flow at Jiangjia Ravine,Yunnan,China:A Field Measurement Using Two Radar Velocimeters

Characteristics of planar velocity distribution of viscous debris flow were analyzed using the measured data at Jiangjia Ravine, Yunnan, China. The velocity data were measured through using two radar velocimeters. The cross-sectional mean velocities were calculated and used to examine Kang et al＇s （2004） relationship, which was established for converting the flow velocity at river centerline measured by a radar velocimeter into the mean velocity based on the stop-watch method. The velocity coefficient, K, defined by the ratio of the mean velocity to the maximum velocity, ranges from 0.2 to 0.6. Kang et al＇s （2004） relationship was found being inapplicable to flows with K smaller than 0.43. This paper contributes to show the complexity of the planar velocity distribution of viscous debris flows and the applicability of Kang et al＇s relationship.