Free vibration analysis of functionally graded CNT-reinforced nanocomposite beam using Eshelby-Mori-Tanaka approach

This work deals with the effect of agglomeration and distribution of carbon nanotube on the free vibration characteristics of a functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) by employing an equivalent fiber based on the Eshelby-Mori-Tanaka approach. Different SWCNTs distributions in the thickness directions are introduced to improve fundamental natural frequency of polymer composite beam. The micromechanics models used in the study include a two parameter model of agglomeration. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler-Bernoulli beam theory. The finite element method is employed to obtain a numerical approximation of the motion equation. Numerical results are presented in both tabular and graphical forms to figure out the effects of nanotube agglomeration, CNTs distribution and boundary conditions on the dynamic characteristics of the beam. The above mentioned effects play very important role on the dynamic behavior of the beam.     

Investigation on steady state deformation and free vibration of a rotating inclined Euler beam

The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite element method combined with floating frame method. The element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The rotating element coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the system are defined in terms of an inertia global coordinate system, which is coincident with a rotating global coordinate system rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.     

A reduced time-varying model for a long beam on elastic foundation under moving loads

Dynamics of a long beam on the elastic foundation subjected to moving loads is studied in the present paper. The sliding window technique is used to dynamically truncate the long beam and a reduced time-varying beam system is obtained. The Hamilton’s principle is employed to establish the equations of motion of the reduced system. The variable separation method is adopted to solve dynamical responses of the reduced system. Examples of a long simply supported Timoshenko beam on the nonlinear foundation subjected to a single moving load and multiple loads are included. Numerical results of the reduced model compared with the ones obtained from the moving element model adapted in literature are carried out to show the validity and the good efficiency of the method proposed in the present paper.     

Dynamic analysis of an axially moving beam subject to inner pressure using finite element method

A dynamic model of an axially moving flexible beam subject to an inner pressure is present. The coupling principle between a flexible beam and inner pressure is analyzed first, and the potential energy of the inner pressure due to the beam bending is derived using the principle of virtual work. A 1D hollow beam element contain inner pressure is established. The finite element method and Lagrange’s equation are used to derive the motion equations of the axially moving system. The dynamic responses are analyzed by Newmark-β time integration method. Based on the computed dynamic responses, the effects of inner pressure on beam dynamics are discussed. Some interesting phenomenon is observed.     

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

In this paper the dynamic response of a simply-supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation acted upon by a moving concentrated force is studied. The Galerkin method is utilized in order to solve the governing equations of motion. Results are compared with the finite element solution for the linear foundation model in order to validate the accuracy of the solution technique. A good agreement between the two solution techniques is observed. The effect of the nonlinearity of foundation stiffness on beam displacement is analyzed for different damping ratios and different speeds of the moving load. The results for the time response of the midpoint of the beam are presented graphically.     

Use of a generalized beam/spring element to analyze natural vibration of rail track and its application

This paper describes the formulation of a generalized beam/spring track element to obtain the natural vibration characteristics of a railway track modeled as a periodic elastically coupled beam system on a Winkler foundation. The rail/tie beams are described by either the Timoshenko beam theory or the Bernoulli-Euler beam theory. The rail beam is assumed to be discretely coupled to the cross-track ties through the coupling spring elements at the periodic rail/tie intersections. The generalized beam/spring element consists of a rail span beam segment, two adjacent tie beams, the coupling spring elements and the ultimate foundation stiffness. The entire track/beam system is then discretized into an assembly of periodic structural units. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the track substructure unit is formulated to establish the dynamic stiffness matrix of the generalized element. The eigenvalue problem of the track/beam system is solved by employing a comprehensive and efficient numerical routine. Solutions are provided for the natural frequencies of the track and the mode shapes of the rail/tie beams under transversely (cross-track) symmetric vibration. The natural vibration results are used to obtain the dynamic receptance response of a typical field track and to compare them with an existing model and field experimental data.     

Study of a hollow laser beam for cladding

Laser cladding, as a promising manufacturing technology, has been widely used in industry for component recovery and surface modification. In this paper, a hollow laser beam was proposed to optimize the laser intensity distribution. A three-dimensional (3-D) finite element (FE) model was developed using ANSYS to investigate the thermal field in the clad deposited by a hollow laser beam. The thermal results, such as the temperature distribution and the cooling rate, were investigated. The effect of the hollow ratio between the inner and outer radius of the hollow beam on the molten pool shape was also studied. The temperature at the boundary of the molten pool was higher than at the center. A clad with a flat metallurgical bonding was formed. The microstructure in the clad was mainly consisted of fine dendrites except the large columnar structures along the bonding. The hardness distribution of the clad was associated with the grain size distribution and the dilution by the substrate. The molten pool was not able to be generated with a high hollow ratio, while overheated at the center with a low hollow ratio. Based on the comparison with the Gaussian laser beam, the hollow laser beam could effectively alleviate the overheating at the center of the clad.     

计及二阶效应的大位移柔性梁杆系统动力学分析

结合小变形条件下梁杆单元精确有限元方法和大位移随动坐标法,建立了计及二阶效应的大位移运动柔性梁单元的动力学方程.首先从小变形结构入手,建立考虑二阶效应的柔性梁压弯力学模型,推导出二阶理论条件下平面压弯梁的精确有限元方程,进而获取二阶理论条件下梁单元精确刚度阵.运用大位移随动坐标法建立大位移几何非线性弹性梁杆单元平衡方程,使用柔性多体动力学的相对描述方法推导大位移梁单元在局部坐标系下的动力学方程.通过结点位移、速度和加速度在随动坐标系与整体坐标系间的相互关系得到梁单元在整体坐标系下的包含二阶效应的动力学方程.对某型港口起重机臂架系统的变幅工况进行了计及二阶效应的弹性动力分析.     

用亚稳态氩原子束制作纳米结构

纳米结构制作是纳米技术的重要组成部分,原子光刻技术是纳米图形制作的一项新方法.对直流高压放电产生的亚稳态氩原子束进行准直减小其发散角,亚稳态原子在与之传播方向垂直的激光驻波场中发生淬火并沉积在基底上,破坏吸附在基底表面的SAM膜(self_assembled monolayers),结合刻蚀技术可制作出纳米量级的图形.给出该技术制作纳米图形的基本原理、方案、相关理论及模拟结果.     

LF6铝镁合金电子束焊接接头的性能与组织初探

分析电子束焊接LF6铝镁合金的焊缝微观组织,研究焊缝中Mg合金元素的烧损现象、焊接接头的力学性能和焊接热裂纹等问题,结果表明,电子束焊接LF6铝镁合金,其焊缝组织为微细等轴晶,熔合线附近为胞状树枝晶;Mg合金元素在焊缝上部和中心区有较大的蒸发损失;焊接接头存在一定的软化,其抗拉强度为母材的91.2％,除延伸率比母材高外,断面收缩率和冲击韧性值与母材相比均有所降低;在合适的参数匹配下,焊缝不会出现热裂纹以及氧化膜所导致的熔合不良与夹渣等问题。     

The mechanical analysis of a mass-spring load supported on a beam system

The static deflection and dynamic characteristics of a mass-spring system supported on beam systems are investigated in this paper. In statics, it shows that the maximum deflection is reduced considerably when a clamped-free beam is replaced by a beam system which consists of a primary beam one end of which is clamped and the other end is supported by a subsidiary beam. The addition of a subsidiary beam leads to axial forces in both beams, the primary one in tension and the subsidiary in compression. The dynamic characteristic shows that the natural frequency of the mass-spring system decreases. In some cases it becomes imaginary, because buckling occurs in the subsidiary beam. This means that the effects of the addition of a subsidiary beam are not always of a positive nature, with respect to the stiffness of the whole system. At low frequencies, the response of the mass is larger than that of the mass supported on a motionless foundation. At high frequencies the dynamic characteristics of the foundation influence the vibration of the mass only a little; i.e. it moves as if the foundation were motionless.     

高功率激光热效应对合束系统的影响

提出利用镀膜合束的方法对三路光束进行合束用于高功率红外激光合束系统设计。考虑系统中关键元件使用的红外材料ZnSe易受热效应影响,采用光机热耦合分析方法,研究了在温度边界条件固定时,各波段激光所产生的耦合热效应对各路激光波前畸变的影响,同时定性分析了系统中存在的激光偏置热效应。研究结果显示,系统中各波段的激光波前畸变均方根值(RMS)均满足设计要求(各波段波前畸变小于λ/8);激光偏置造成的波面高频成分增大了长波激光波前畸变量,但高频成分对系统波前畸变影响依然满足要求;轴向温差可在35s达到平衡,对光束波前造成主要影响的是各块镜片的面型畸变。根据分析结果搭建了实验平台,利用系统中短波400 W激光进行实验,采集了该条件下的面型并与仿真结果进行了对比,实验结果验证了该分析方法计算结果的准确性。     

Electron beam processed surface textures on titanium alloys for fluid-drag reduction

Ti-6Al-4V and Ti-4Al-1.5Mn alloys were employed for electron beam processing with the aim to produce surface textures efficient for fluid-drag reduction. The as-resulted surface textures were examined by using advanced optical microscopy for surface morphology analysis, optical microscopy and scanning electron microscopy for near-surface microstructure observation. The titanium model with electron beam processed surface textures was tested in wind tunnel to evaluate their fluid-drag reduction efficiency. It showed that the as-resulted non-smooth surface was characterized by parallel ridges and grooves, with height and spacing able to be customized by adjusting processing parametres. The ridges displayed continuous scales while the valley of grooves presented V-shaped ripples. Their dimensions were also related to and could be controlled by processing parametres. Further, the near-surface region was occupied by fusion zone, heat-affected zone and base metal from the outermost surface to the underlying bulk alloy. The microstructure of fusion zone was characterized by martensite phase. A heat-affected zone was sandwiched between fusion zone and the underlying base metal, with different microstructural features compared to both fusion zone and the base metal. With respect to fluid-drag reduction efficiency, titanium model with electron beam processed surface textures exhibits a reducing efficiency over 15% at attack angles of 0° and ±1°, with an air flow velocity at 24 m/s.     

Spectral element modeling and analysis of the dynamics and guided waves in a smart beam with a surface-bonded PZT layer

To predict ultrasonic guided waves generated by a piezoelectric transducer (PZT) in a structure accurately, the dynamic coupling between the base structure and the surface-bonded PZT must be modeled accurately and analyzed in an efficient way. For so-called smart beams, which consist of a metallic base beam and a surface-bonded PZT layer, we propose a spectral element model that has the capability to accurately predict high frequency dynamic responses and guided waves. For the spectral element model, Timoshenko beam theory is applied to both the base beam and PZT layer, and Mindlin-Herrmann rod theory is adopted to account for the effects of lateral contraction in the thickness direction of the base beam. The high accuracy of the spectral element model is validated by comparing the results of the spectral element model with conventional finite element method (FEM) results and results from the commercial finite element analysis package ANSYS. The effects of PZT-induced axial-bending coupling and structural damping on the dynamics and guided waves are then investigated using numeral simulation.     

离子辅助制备碳化硅改性用硅膜的研究

本文介绍了一种利用霍尔型离子源辅助电子束蒸发，在碳化硅（Silicon Carbide: SiC）材料上制备硅改性薄膜的方法，研究了不同沉积速率下改性后的抛光效果。对样品进行了表面散射及反射的测量。通过样品的显微照片可知硅膜层在沉积速率增大条件下结构趋于疏松。通过精细抛光改性的反应烧结碳化硅（Reaction Bonded Silicon Carbide: RB-SiC）样品表面散射系数减小到1.46%，反射率接近抛光良好的微晶玻璃。温度冲击实验和表面拉力实验表明硅膜无龟裂和脱落，性质稳定，与碳化硅基底可以良好的结合。     

Some studies on temperature profiles in AISI 304 stainless steel sheet during laser beam welding using FE simulation

The investigation of transient temperature profiles of a weld joint produced by the laser welding process is presented. A three-dimensional finite element model is developed using a commercial finite element code ANSYS in order to obtain the behavior of temperature field and molten pool shape during the welding process. A three-dimensional conical Gaussian heat source is employed as a heat source model for performing a non-linear transient thermal analysis. The temperature-dependent material properties of AISI 304 stainless steel sheet are taken into account, which has a great influence on the temperature fields indicated by the simulation results. The effect of latent heat and the convective and radiative boundary conditions are also included in the model. A series of laser welds are performed using a 2-kW continuous wave Nd:YAG laser welding system. The experimental trials are conducted by varying the laser input parameters namely beam power, welding speed, and beam incident angle to validate the model. The results show that there is a good agreement between the finite element simulation and the experimental observations.     

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Winkler foundation and Euler-Bernoulli beam on Pasternak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated.     

Dynamic analysis of composite beam subjected to harmonic moving load based on the third-order shear deformation theory

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the third-order shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to demonstrate the accuracy of the present method, the results TSDT are compared with the previously obtained results based on first-order shear deformation theory, with which good agreements are observed.     

Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory

Nonlinear free vibration and instability of fluid-conveying double-walled boron nitride nanotubes (DWBNNTs) embedded in viscoelastic medium are studied in this paper. The effects of the transverse shear deformation and rotary inertia are considered by utilizing the Timoshenko beam theory. The size effect is applied by the modified couple stress theory and considering a material length scale parameter for beam model. The nonlinear effect is considered by the Von Kármán type geometric nonlinearity. The electromechanical coupling and charge equation are employed to consider the piezoelectric effect. The surrounding viscoelastic medium is described as the linear visco-Pasternak foundation model characterized by the spring and damper. Hamilton’s principle is used to derive the governing equations and boundary conditions. The differential quadrature method (DQM) is employed to discretize the nonlinear higher-order governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequency and critical fluid velocity of fluid-conveying DWBNNTs with clamped-clamped (C-C) boundary conditions. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, spring and damping constants of surrounding viscoelastic medium and fluid velocity on the nonlinear free vibration, instability and electric potential distribution of DWBNNTs. This study might be useful for the design and smart control of nano devices.     

Static analysis of a Bickford beam by means of the DQEM

In this paper the recently proposed differential quadrature element method is employed in order to solve the equilibrium equations of a higher-order beam. A simple five-node element is introduced, in which the vertical displacement is approximated by a sixth-order polynomial, whereas the rotation is consistently approximated by a fourth-order polynomial, and the resulting weighting coefficient matrix is given. Moreover, a general procedure is outlined, for an N-node element, in which vertical displacements and rotations are given by polynomials of order N+1 and N-1, respectively. Numerical examples are aimed both at checking the convergence of the results for increasing values of the nodes, and at comparing the used cubic beam theory with the simpler, linear, Timoshenko theory.