Nonlinear vibration and rippling instability for embedded carbon nanotubes

Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of single-walled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio, and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.     

Nonlinear viscose flow induced nonlocal vibration and instability of embedded DWCNC via DQM

Nonlinear thermo free vibration and instability of viscose fluid-conveying double-walled carbon nanocones (DWCNCs) are studied using Hamilton’s principle and differential quadrature method (DQM). The small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number (Kn) is considered. The nanocone is simulated as a clamped-clamped Euler-Bernoulli’s beam embedded in an elastic foundation of the Winkler and Pasternak type. The van der Waals (vdW) forces between the inner and outer nanocones are taken into account. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, apex angles, aspect ratio, temperature change, fluid viscosity, boundary conditions and the elastic medium coefficient on the dimensionless frequency and critical fluid velocity of DWCNCs. The results show that the small-size effect on flow field is remarkable on frequency and critical fluid velocity of DWCNC. Also, the nonlinear frequency and critical flow velocity decrease with increasing the nonlocal parameter and cone semi-vertex angle. The results are in good agreement with the previous researches.     

Modeling the effect of intermolecular force on the size-dependent pull-in behavior of beam-type NEMS using modified couple stress theory

Experimental observations reveal that the physical response of nanostructures is size-dependent. Herein, modified couple stress theory has been used to study the effect of intermolecular van der Waals force on the size dependent pull-in of nanobridges and nanocantilevers. Three approaches including using differential transformation method, applying numerical method and developing a simple lumped parameter model have been employed to solve the governing equation of the systems. The pull-in parameters i.e. critical tip deflection and instability voltage of the nanostructures have been determined. Effect of the van der Waals attraction and the size dependency and the importance of coupling between them on the pull-in performance have been discussed.     

Structural instability of carbon nanotubes embedded in viscoelastic medium and subjected to distributed tangential load

In this paper, the nonlocal Euler-Bernoulli beam model is used to predict the static and dynamic structural instability of carbon nanotubes (CNTs) subjected to a distributed tangential compressive load. The CNT is considered to be embedded in a Kelvin-Voigt viscoelastic medium. Equation of motion and boundary conditions are obtained using the extended Hamilton’s principle and the extended Galerkin’s method is applied in order to transform the resulting equations into a general eigenvalue problem. The derived equations are validated by comparing the results achieved from the new derivations with existing solutions in literature. Effects of several experimentally interesting boundary conditions are considered on the stability characteristics of the CNT. Moreover, the influences of small scale parameter and material properties of the surrounding viscoelastic medium on the stability boundaries are examined.     

Nonlinear stability boundary of journal bearing systems operating with non-Newtonian couple stress fluids

The non-Newtonian effects on the nonlinear stability boundary of short journal bearings are investigated through the transient nonlinear analysis. Two coupled nonlinear equations are solved by using the fourth-order Runge-Kutta method. According to the results, there exists a nonlinear stability boundary within the clearance circle. Any initial positions of the shaft center outside of this boundary would yield an unstable trajectory, even though the bearing should be stable in accordance with the linear stability theory. The non-Newtonian effects provide a larger stability boundary within the clearance circle as compared to the bearing lubricated with a Newtonian fluid.     

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded orthotropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.     

Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory

The small-scale effect on the torsional buckling of a double-walled carbon nanotube (DWCNT) embedded on Winkler and Pasternak foundations is investigated in this study using the theory of nonlocal elasticity. The effects of the surrounding elastic medium, such as the spring constant of the Winkler type and the shear constant of the Pasternak type, as well as the van der Waals (vdW) forces between the inner and the outer nanotubes are taken into account. Finally, based on the theory of nonlocal elasticity and by employing the continuum models, an elastic double-shell model is presented for the nonlocal torsional buckling load of a DWCNT. It is seen from the results that the shear constant of the Pasternak type increases the nonlocal critical torsional buckling load, while the difference between the presence and the absence of the shear constant of the Pasternak type becomes large. It is shown that the nonlocal critical buckling load is lower than the local critical buckling load. Moreover, a simplified analysis is carried out to estimate the nonlocal critical torque for the torsional buckling of a DWCNT.     

微机械角振动谐振器在低气压下的非线性振动

本文研究气压对微机械角振动谐振器振动特性的影响。基于谐振器的梁的弹性力矩和角位移之间的3次多项式关系,建立了谐振器非线性振动方程。给出了谐振器自然频率与振幅的关系和频率响应特性与振幅关系的理论解。测试了在大气压、1100Pa和130Pa下谐振器的频率响应曲线。通过对大气压下振动频率特性的分析,得到了非线性振动方程的基本参数,将这些参数和低气压小振幅下的品质因数代入频率特性的理论解,推算出的低气压大振幅下的频率特性与实测曲线符合。随着气压的降低,谐振器振动频率响应的非线性程度增大。     

Separation of a sphere from a flat in the presence of couple stress fluids

A mathematical model for couple stress fluid is presented to analyse the separation flow of a fully flooded sphere from a flat under the condition of constant load. Assuming the lubricant between the sphere and the flat to contain additives, the couple stress effect, presented by the characteristic length of the additives, has been considered to account for the non‐Newtonian behaviour. In addition, the effect of the sphere inertia on accelerating the separation process has been considered. Compared with the Newtonian fluid case, the results of the numerical solution indicated that the separation time increases with increasing the characteristic length of the additives. It was also found that the additive characteristic length has negligible effect on the thickness of the lubricant film at the separation point. Copyright © 2007 John Wiley & Sons, Ltd.     

滚动轴承振动与噪声关系的灰分析

以灰色系统理论为基础，通过实验研究6201和6203轴承振动与噪声的灰色关联性。振动用加速度值描述，噪声指声压级。实验数据处理结果表明，轴承振动与噪声的关系不明显并具有很大的不确定性，有时轴承振动与噪声之间会出现系统性误差。因此，不宜用轴承的振动代替轴承的噪声，应单独研究轴承的噪声问题，制订轴承噪声标准和相应的工艺标准。     

Nonlinear analysis of the buckling and vibration of a rotating elasticum

We investigate the static and dynamic behaviour of an elasticum which is clamped radially to the inside of a rotating ring and carries a mass at the free end. A nonlinear model for buckling and vibration of the structure in the plane of the ring is established and a subsequent Galerkin procedure leads to a system of two first order ODEs, accessible to a bifurcation and phase plane analysis. It will be shown that these results can only claim limited validity. Afterwards, more adequate results are obtained by a Poincaré-Lindstedt perturbation method. This approach is possible, since the linearized model equation can be solved analytically. Regarding the angular velocity of the ring as a bifurcation parameter, the analysis shows the existence of a supercritical bifurcation for any length of the elasticum. Finally, the case of out-of-plane buckling is shortly investigated, with the result that no buckling occurs for a sufficiently long elasticum.     

Investigation of buckling of double-walled carbon nanotubes embedded in an elastic medium using the energy method

Elastic buckling of a long double-walled carbon nanotube embedded in an elastic medium and subjected to a far-field hydrostatic pressure is analyzed using the energy method. The study is on the basis of elastic-shell models at nano-scale, and the effect of van der Waals forces on the buckling is considered. The double-walled carbon nanotube is assumed to be thin and the tube is taken to be perfectly bonded to the surrounding medium. Both normal and shear stresses at the outer tube-medium interface are included. The difference between the Poisson's ratio of the tube and that of the elastic medium is taken into account. An expression is derived relating the external pressure to the buckling mode number, from which the critical pressure can be obtained. As a result, the critical pressure is dependent on the inner radius-to-thickness ratio, the material parameters of the elastic medium, and the van der Waals force.     

Electro-thermo nonlocal nonlinear vibration in an embedded polymeric piezoelectric micro plate reinforced by DWBNNTs using DQM

In the present paper, electro-thermo nonlinear vibration of a piezo-polymeric rectangular micro plate made from polyvinylidene fluoride (PVDF) reinforced by zigzag double walled boron nitride nanotubes (DWBNNTs) is studied. This plate is embedded in an elastic medium which is simulated by Winkler and Pasternak foundation models. Using nonlinear strain-displacement relations and nonlocal elasticity plate theory as well as considering charge equation for coupling between electrical and mechanical fields, the motion equations are derived based on energy method and Hamilton??s principle. The differential quadrature method (DQM) is employed to computation of nonlinear frequency for different mechanical and free-free electrical boundary conditions. The results indicate that smart composite and consequently the generated G4 improved sensor and actuator applications in several process industries, because it increases the nonlinear vibration frequency. Furthermore, it can be also found that the nonlinear frequency increases as the values of the elastic medium constants, the geometrical aspect ratios and DWBNNTs volume fraction increase but it decreases as nonlocal parameter increases.     

Inertia force effects in the non-Newtonian couple stress squeeze film between a sphere and a flat plate

On the basis of the Stokes micro-continuum theory together with the method of mean averaged inertia, the influences of fluid inertia forces on the non-Newtonian squeeze film characteristics between a sphere and a flat plate have been presented. Comparing with the case of a non-inertia non-Newtonian lubricant, the consideration of fluid inertia forces provides a longer squeeze film time especially for the squeeze film operating with a lower film height, and a larger non-Newtonian parameter and density parameter. It prolongs the life of squeeze films.     

嵌入式便携数据采集分析仪的设计与实现

研制了一种以SAMSUNG公司的ARM9芯片S3C2410为硬件核心、以ARM-LINUX为操作系统软件平台、面向工程设备故障诊断的便携式振动数据采集分析仪.在北京某软件公司提供的图形中间件MiniGUI的基础上,利用C语言开发了数据分析系统作为图形用户界面.重点介绍了硬件各个主要功能模块的组成和工作原理,以及系统软件的构架与功能.该系统集数据采集、分析与数据通信于一体,具有图形界面友好、操作方便、存储容量大、采集精度高、数据回收与点检任务管理方便的特点.     

Experimental study on a noncontact method using laser displacement sensors to measure vibration stress in piping systems

This study presents a noncontact measurement method of vibration induced stress (vibration stress) using multiple laser displacement sensors and clarifies its applicability to piping vibration. In the beam structures such as piping, the stress due to bending deformation can be caused by vibration. In the presented method, the vibration displacement in the beam structures induced by the bending deformation is measured at three different locations using laser displacement sensors in a noncontact manner and the vibration stress is estimated by a simple calculation based on the beam theory. First, an applicability validation of the presented method was done by a vibration test using a cantilevered beam plate. This validation was done by comparing measurements by the presented method and the conventional method using strain gauges. Next, an experimental validation was conducted by the vibration test using a pipe specimen, and the applicability to the piping vibration was confirmed.     

Application of Dempster–Shafer theory in fault diagnosis of induction motors using vibration and current signals

This paper presents an approach for the fault diagnosis in induction motors by using Dempster–Shafer theory. Features are extracted from motor stator current and vibration signals and with reducing data transfers. The technique makes it possible for on-line application. Neural network is trained and tested by the selected features of the measured data. The fusion of classification results from vibration and current classifiers increases the diagnostic accuracy. The efficiency of the proposed system is demonstrated by detecting motor electrical and mechanical faults originated from the induction motors. The results of the test confirm that the proposed system has potential for real-time applications.     

非线性振动理论在振动输送机中的研究与应用

在线性振动输送机的基础上，引入非线性振动理论，研究弹性力为连续变化的非线性硬特性线变节距弹簧在变载荷系统中的应用，实现系统刚度随载荷基本呈线性变化，使得系统振幅较线性振动输送机要稳定得多，可真正实现系统在近共振点附近运行，并可方便地利用调整弹簧预紧量的办法改变系统的工作点。     

Study of flow instability in a centrifugal fan based on energy gradient theory

Flow instability in a centrifugal fan was studied using energy gradient theory. Numerical simulation was performed for the threedimensional turbulent flow field in a centrifugal fan. The flow is governed by the three-dimensional incompressible Navier-Stokes equations coupled with the RNG k-ε turbulent model. The finite volume method was used to discretize the governing equations and the Semi-implicit method for pressure linked equation (SIMPLE) algorithm is employed to iterate the system of the equations. The interior flow field in the centrifugal fan and the distribution of the energy gradient function K are obtained at different flow rates. According to the energy gradient method, the area with larger value of K is the place where the flow loses stability easier. The results show that instability is easier to generate in the regions of impeller outlet and volute tongue. The air flow near the hub is more stable than that near the shroud. That is due to the influences of variations of the velocity and the inlet angle along the axial direction. With the decrease of the flow rate, instability zone in a blade channel moves to the impeller inlet from the outlet and the unstable regions in different channels develop in opposite direction to the rotation of impeller.     

Nonlinear deterministic analysis of tissue texture: a stereological study on mastopathic and mammary cancer tissue using chaos theory

Signals from some dynamical systems look like stochastic processes although their latent mechanism is deterministic. When such systems show sensitive dependence on small changes of initial conditions, they are denoted as deterministic chaos. Motivated by recent advances in statistical inference methods for chaotic systems and by the concept of spatial chaos, we present a deterministic approach to the study of epithelial tissue texture. Methods for estimation of the autocorrelation function, for evaluation of the power spectrum, for attractor reconstruction, for estimation of the Lyapunov exponent and of the correlation dimension, and for the generation of surrogate data sets are outlined. In our biological example, these methods are applied to 20 cases of mastopathy as compared to 20 cases of mammary cancer. The input signals for the analysis were estimates of epithelial fraction measured at low magnification within 5100 equally spaced line segments per case perpendicular to an arbitrarily directed axis. The results suggest the existence of a low-dimensional deterministic attractor in mastopathic tissue texture, which is replaced by coloured noise in the majority of mammary carcinomas. Biological mechanisms for this finding and scale effects are discussed, and some methodological aspects and possible extensions of our approach are outlined.