A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid

In this paper, a new, modified nonlocal beam model is developed for analyzing the vibration and stability of nanotubes conveying fluid, in which one single nonlocal nanoscale parameter is included. Using Hamilton’s principle, a new higher-order differential equation of motion and the corresponding higher-order, non-classical boundary conditions are obtained for nanotubes conveying fluid. Based on this modified nonlocal model, effect of nonlocal nanoscale parameter on natural frequencies and critical flow velocities is presented and discussed through numerical calculations. It is found that this factor has great influence on the vibration and stability of nanotubes conveying fluid. In particular, the nonlocal effect tends to induce higher natural frequencies and higher critical flow velocities as compared to the results obtained from the classical and partial nonlocal beam models.     

In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium

The effect of the induced vibrations in the carbon nanotubes (CNTs) arising from the internal fluid flow is a critical issue in the design of CNT-based fluidic devices. In this study, in-plane vibration analysis of curved CNTs conveying fluid embedded in viscoelastic medium is investigated. The CNT is modeled as a linear elastic cylindrical tube where the internal moving fluid is characterized by steady flow velocity and mass density of fluid. A modified-inextensible theory is used in formulation and the steady-state initial forces due to the centrifugal and pressure forces of the internal fluid are also taken into account. The finite element method is used to discretize the equation of motion and the frequencies are obtained by solving a quadratic eigenvalue problem. The effects of CNT opening angle, the elastic modulus and the damping factor of the viscoelastic surrounded medium and fluid velocity on the resonance frequencies are elucidated. It is shown that curved CNTs are unconditionally stable even for a system with sufficiently high flow velocity. The most results presented in this investigation have been absent from the literature for fluid-induced vibration of curved CNTs embedded in viscoelastic foundations.     

Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid

The flexural vibration of viscoelastic carbon nanotubes (CNTs) conveying fluid and embedded in viscous fluid is investigated by the nonlocal Timoshenko beam model. The governing equations are developed by Hamilton's principle, including the effects of structural damping of the CNT, internal moving fluid, external viscous fluid, temperature change and nonlocal parameter. Applying Galerkin’s approach, the resulting equations are transformed into a set of eigenvalue equations. The validity of the present analysis is confirmed by comparing the results with those obtained in literature. The effects of the main parameters on the vibration characteristics of the CNT are also elucidated. Most results presented in the present investigation have been absent from the literature for the vibration and instability of the CNT conveying fluid.     

Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory

A nonlocal Euler–Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid.     

Dynamics of arrays of cylinders with internal and external axial flow

Various aspects of the dynamics and stability of clusters of tubular cylinders containing internally flowing fluid and surrounded by a bounded external axial flow are examined. The general character of free motions is established by obtaining the eigenfrequencies of the system and studying their evolution with increasing flow, internal or external. Stability diagrams have been obtained for the critical flow velocities, beyond which the system would lose stability by buckling (divergence), under the combined effect of internal and external flow. Free vibration, following an initial disturbance of one of the cylinders, is studied, in order further to examine the effect of hydrodynamic coupling. It is found that beating phenomena may arise, implying energy transfer between cylinders and the possibility of transient amplitudes much larger than the initial disturbances. Also, the vibration of the system (in still fluid) when one cylinder is constrained to oscillate in a prescribed manner is examined, establishing that transmission of vibration from cylinder to cylinder can be very rapid; indeed, such constrained motion of one cylinder at certain frequencies may induce large amplified motions of others.     

Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory

A nonlocal Euler–Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid.     

The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Dynamic stability of elastically supported pipes conveying pulsating fluid

The effect of support flexibility on the dynamic behaviour of pipes conveying fluid is investigated for both steady and pulsatile flows. The pipes are built-in at the upstream end and supported at the other by both a translational and a rotational spring. For the steady flow condition, the critical flow velocities, the frequencies and flow induced damping patterns that are associated with the different vibration modes of selected pipe systems are determined as functions of the flow velocity. The results from steady flow cases show that the pipes may first lose stability by either buckling or flutter, depending on the values of the rotational and translational spring constants and their relative magnitudes. In the case of pulsatile flow, the Floquet theory is utilized for the stability analysis of the selected pipe-fluid systems. Numerical results are presented to illustrate the effects of the amount of translational and rotational resiliences at the elastic support on the regions of parametric and combination resonances of the pipes. The results more of the interesting aspects of the behaviour of non-conservative systems.     

H-infinity optimization of a variant design of the dynamic vibration absorber—Revisited and new results

The H_∞ optimum parameters of a dynamic vibration absorber (DVA) with ground-support are derived to minimize the resonant vibration amplitude of a single degree-of-freedom (sdof) system under harmonic force excitation. The optimum parameters which are derived based on the classical fixed-points theory and reported in literature for this non-traditional DVA are shown to be not leading to the minimum resonant vibration amplitude of the controlled mass. A new procedure is proposed for the H_∞ optimization of such a dynamic vibration absorber. A new set of optimum tuning frequency and damping of the absorber is derived, thereby resulting in lower maximum amplitude responses than those reported in the literature. The proposed optimized variant DVA is also compared to a ground-hooked damper of the same damping capacity of the damper in the DVA. It is proved that the proposed optimized DVA has better suppression of the resonant vibration amplitude of the controlled system than both the traditional DVA and also the ground-hooked damper if the proposed design procedure of the variant DVA is followed.     

Use of modal energy transfer as a new damping device with controllable bandwidth

This paper presents a new design of nonlinear dynamic absorber (NDA) using the phenomenon of modal energy transfer between the symmetric mode and the anti-symmetric mode of a curved beam. It can reduce the resonance vibration of a primary structure with a controllable operational frequency range. The energy transfer is initiated by an autoparametric vibration and the excitation force required is lowest when the ratio of the resonance frequencies of the first symmetric mode (ω₁) and first anti-symmetric mode (ω₂) is close to 2.The resonance frequency of the first anti-symmetric mode (ω₂) can be altered to control the operational frequency range. The autoparametric vibration response can be used to create an energy-dissipative region with a controllable bandwidth. It is also possible to create a non-dissipative region in between two dissipative regions. This is useful for providing damping for a conventional dynamic absorber without adding high damping material. The damping is due to the dissipation of energy to anti-symmetric mode. Numerical calculations indicate that the resonance vibration of a primary structure can be successfully reduced using this approach. The results are verified with experimental data.     

Effects of internal viscous damping on the stability of a rotating shaft driven through a universal joint

A rotating flexible shaft, with both external and internal viscous damping, driven through a universal joint is considered. The mathematical model consists of a set of coupled, linear partial differential equations with time-dependent coefficients. Use of Galerkin's technique leads to a set of coupled linear differential equations with time-dependent coefficients. Using these differential equations some effects of internal viscous damping on parametric and flutter instability zones are investigated by the monodromy matrix technique. The flutter zones are also obtained on discarding the time-dependent coefficients in the differential equations which leads to an eigenvalue analysis. A one-term Galerkin approximation aided this analysis. Two different shafts (“automotive” and “lab”) were considered. Increasing internal damping is always stabilizing as regards to parametric instabilities. For flutter type instabilities it was found that increasing internal damping is always stabilizing for rotational speeds v below the first critical speed, v₁. For v>v₁, there is a value of the internal viscous damping coefficient, C_iv, which depends on the rotational speed and torque, above which destabilization occurs.The value of C_iv (“critical value”) at which the unstable zone first enters the practical range of operation was determined. The dependence of C_iv critical on the external damping was investigated. It was found for the automotive case that a four-fold increase in external damping led to an increase of about 20% of the critical value. For the lab model an increase of two orders of magnitude of the external damping led to an increase of critical value of only 10%.For the automotive shaft it was found that this critical value also removed the parametric instabilities out of the practical range. For the lab model it is not always possible to completely stabilize the system by increasing the internal damping. For this model using C_iv critical, parametric instabilities are still found in the practical range of operation.     

Impact and vibration testing of shipping containers

Equations are developed for experimental evaluation of restoring and dissipative parameters, as used in a non-linear mathematical unit load model. A specially developed transportation damage simulation test jig is described. This jig is suitable for impact and vibration load reproduction on bottom tier containers in unit loads, but only a single container sample is needed. A detailed case study is described, exemplifying how these parameters may be evaluated by impact (shock) or vibration testing of corrugated produce shipping containers. The initial spring rate K₀ was found to be approximately equal in impact and vibration loading. The parameter r, expressing the non-linearity, was significantly larger in vibration loading than in impact loading. On the other hand, both viscous and Coulomb damping are significantly greater in impact loading than in vibration loading. The same modus operandi may be used for determination of dynamic restoring and dissipative parameters of other products, such as cushioning foams and elastomers.     

Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability

This paper initiates the theoretical analysis of microscale resonators containing internal flow, modelled here as microfabricated pipes conveying fluid, and investigates the effects of flow velocity on damping, stability, and frequency shift. The analysis is conducted within the context of classical continuum mechanics, and the effects of structural dissipation (including thermoelastic damping in hollow beams), boundary conditions, geometry, and flow velocity on vibrations are discussed. A scaling analysis suggests that slender elastomeric micropipes are susceptible to instability by divergence (buckling) and flutter at relatively low flow velocities of ∼10 m/s.     

Effect of boundary layer thickness before the flow separation on aerodynamic characteristics and heat transfer behind an abrupt expansion in a round tube

Results of numerical investigation of the boundary layer thickness on turbulent separation and heat transfer in a tube with an abrupt expansion are shown. The Menter turbulence model of shear stress transfer implemented in Fluent package was used for calculations. The range of Reynolds numbers was from 5·10³ to 105. The air was used as the working fluid. A degree of tube expansion was (D ₂/D ₁)² = 1.78. A significant effect of thickness of the separated boundary layer both on dynamic and thermal characteristics of the flow is shown. In particular, it was found that with an increase in the boundary layer thickness the recirculation zone increases, and the maximum heat transfer coefficient decreases. The work was financially supported by the Russian Foundation for Basic Research (project codes 07-08-00025 and 06-08-00300).     

基于Timoshenko梁模型的周期充液管路弯曲振动带隙特性和传输特性

充液管路的固液耦合振动广泛存在于各种工程领域中,对其弯曲振动控制进行研究具有重要意义.将声子晶体的周期性思想引入到管路结构设计中,将管壁设计成沿轴向交替排列的周期性复合结构.基于Timoshenko梁模型,采用传递矩阵法计算了固液耦合条件下周期管路结构的弯曲振动能带结构及其传输特性,同时分析了材料阻尼系数、周期和非周期支撑对带隙特性的影响.充液周期管路结构的弯曲振动带隙特性为管路的振动控制提供了一条新的技术途径. 关键词： 声子晶体 充液管路 振动带隙     

Flames in narrow circular tubes

We examine an axi-symmetric deflagration located in a tube with thermally active walls. It is noted that the flame-in-tube configuration defines a classical edge-flame, a flame in a shear flow for which there is a water-shed solution for a critical value of the Damköhler number (D), ignition front solutions for larger values of D, and failure wave solutions for smaller values. We examine semi-infinite tubes with a heat flux imposed at the tube wall ends, to simulate experiments reported in the 30th Symposium. We identify parameters for which stable solutions are obtained at certain flow rates, but unstable solutions are generated at higher flow rates, followed by stable solutions at still higher flow rates. These solutions are consistent with the experimental record. Instability leads either to regular oscillations or to a violent process characterized by quenching and re-ignition.     

Burning velocity of triple flames with gentle concentration gradient

We investigated the local flame speed of a two-dimensional, methane-air triple flame in a rectangular burner. The velocity fields and the concentration profiles were measured with particle image velocimetry and the Rayleigh scattering method, respectively. There was a requisite combination of initial velocity and initial concentration gradient for consistency of the local concentration gradient at the leading edge of the flame. In these cases, the flame curvatures were also consistent. Accordingly, the burning velocity, defined as local flow velocity at the triple point, was determined by the flame curvature. The burning velocity increased with increasing flame curvature, when the curvature was near zero. After that, the burning velocity decreased with increasing curvature. The peak value thus exceeded the adiabatic one-dimensional laminar burning velocity. Comparing the effects of the measured flame stretch rate on the flow strain κ_s and flame curvature κ_c, κ_s is larger and increases more rapidly than κ_c for flame curvatures satisfying 1/R_f < 250 m⁻¹ and then becomes constant while κ_c still increases for 250 m⁻¹ < 1/R_f, so that κ_c becomes much larger than κ_s. There is also a peak in burning velocity at roughly the transition in flame curvature specified above. Therefore, the burning velocity for a low concentration gradient correlates with the flame stretch rate.     

Magnetic properties of iron nitride films prepared by oblique sputtering under different nitrogen gas flow ratios (N2/N2+Ar)

Iron nitride thin films were prepared on Si (100) substrates by oblique radio-frequency reactive magnetron oblique sputtering. Structures, phases and magnetic properties were investigated as a function of nitrogen gas flow ratio F_N(F_N=F_N2/(F_N2+F_Ar)×100%). When F_N is in the range of 2–7%, the iron nitride films show amorphous or nano-crystalline structures, which exhibit good soft magnetic properties. With 3%≤F_N≤6%, films show in-plane uniaxial magnetic anisotropy. Both intrinsic damping factor α_in and extrinsic damping factor α_ex of the iron nitride films increase with increasing F_N. The film deposited under F_N=6% with the resonance frequency f_r=3.3 GHz and full width at half-maximum Δf=3.6 GHz has great potential for high-frequency electromagnetic shielding applications.     

A finite element computation of the flow-induced oscillations in a cantilevered tube

A numerical method is presented for predicting the response of a cantilevered tube conveying fluid. Emphasis is placed on the oscillation amplitude, dominant frequency, and response mode shapes for flow velocities larger than the critical values. Numerical results and experimental data agree reasonably well.     

Diffusion in a tube consisting of alternating wide and narrow sections

The problem of the diffusion of particles in a tube consisting of identical units, each composed of a wide and narrow section is solved. With an approach based on reducing the problem to a one-dimensional, the statistics of times of particle transition between adjacent sections is determined, which is a detailed characteristic of the diffusion process. An expression for the effective diffusion coefficient D _ef , defining the slow-down of transport due to variations of the tube profile, is derived. It is shown that D _ef behaves monotonically with increasing length of both the narrow and wide sections. The predictions of analytical formulas are in good agreement with the results of computer simulation performed by the Brownian dynamics method.