Effects of local thickness defects on the buckling of micro-beam

A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity. By introducing the local thickness defects function of the micro-beam, the variable coe-cient differential equations of the buckling problem are obtained with the variational principle. Combining the eigensolution series of the complete micro-beam with the Galerkin method, we obtain the critical load and buckling modes of the micro-beam with defects. The results show that the depth and location of the defect are the main factors affecting the critical load, and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam. The effect of defect location on buckling is related to the axial gradient of the rotation angle, and defects should be avoided at the maximum axial gradient of the rotation angle. The model and method are also applicable to the static deformation and vibration of the micro-beam.     

Acoustic waves in two-fraction mixtures of gas with vapor,droplets and solid particles of different materials and sizes in the presence of phase transitions

The propagation of acoustic waves in two-fraction mixtures of gas with vapor, droplets and solid particles of different materials and sizes in the presence of phase transitions is investigated. A mathematical model is presented, the dispersion and wave equations are obtained, and the dispersion curves are calculated. The relative sonic velocity and the attenuation decrement on the wave length are analyzed as functions of the oscillation frequency for an “air-vapor-liquid droplet-sand particle” mixture. Using the fast Fourier transform, the propagation of pulse disturbances in the two-fraction disperse systems is calculated.     

鳗鲡模式游动的鱼体变形曲率波的传播特性研究

将鳗鲡模式游动的七鳃鳗简化成材料性质均匀的变截面黏 弹性梁,通过数值方法求解鱼体在主动弯矩波(作为激励的驱动波)的驱动下匀速游动时身体变形曲率波的传播特性. 结果表明,当主动弯矩 的驱动频率高于鱼体结构基频时,可以观察到曲率波相对于驱动波存在相位滞后,且越靠近尾部滞后现象越明显,这意味着曲率波的波速 小于驱动波的波速,也间接地验证了前人的实验结果. 通过参数研究发现,鱼体变形曲率波与驱动波的波速比与表征流体黏性作用的雷诺数无关,而与表征驱动波和鱼体材料属性的 无量纲激励频率、激励波长及鱼体黏性系数有关. 对于鳗鲡模式游动的鱼类,曲率波与驱动波的波速比随着无量纲激励频率和波长的增大而降低,随着鱼体黏性系数的增大而增大. 进一步研究发现,通过小扰动分析得到的组合相似性参数$\varPi$可以统一描述波速比与激励参数、材料参数之间的关系.      

空气耦合层状复合材料的声传播研究

本文研究了空气耦合层状复合材料的声传播。从基本波动方程出发,由气固边界条件,利用势函数法求解声波任意角入射层状复合材料的声传播,并通过数值计算得到其透声系数幅度和相位随频率变化的规律。基于MATLAB建立了测量任一入射角透声系数的实验平台,并对复合材料试样进行了实验,得到的透声系数幅度与理论计算结果吻合,说明了所建立的声传播理论和实验检测方法的有效性。     

Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric(FGP) nanoplates deposited in a viscoelastic foundation. It is assumed that(i) the material parameters of the nanoplates obey a power-law variation in thickness and(ii) the uniform porosity exists in the nanoplates. The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined hi...     

PWAS激励Lamb波的谱有限元建模及参数研究

基于谱有限元法发展了一种由压电晶片主动传感器(PWAS)、胶层和主结构组成的三层模型,来模拟PWAS激励结构中Lamb波的传播。首先在各层使用不同的梁理论,推导PWAS-胶层-主结构三层模型的控制方程和力的边界条件,建立谱有限元模型。通过和传统的有限单元法进行比较,表明了在显著提高计算效率的同时,所发展谱有限元模型在分析结构中Lamb波传播上仍具有较高的精度。分析了激励频率、PWAS长度与厚度、胶层厚度等参数变化对输出电压信号的影响,可以为基于PWAS和Lamb波的主动健康监测技术提供参考。     

含环向表面裂纹圆柱壳的波传播特性研究

研究了振动波在含有环向表面裂纹的无限长圆柱壳中的传播特性.圆柱壳体的振动用Flügge方程来描述.运用线弹性断裂力学的理论,考虑到裂纹的张开、滑移和撕裂3种模式以及它们相互之间的耦合,利用分布的线弹簧来模拟裂纹并建立了裂纹所在区域的局部柔度矩阵,得到由此引起的附加位移和壳体中内力之间的关系.在入射波已知的情况下,根据裂纹两侧区域的位移和内力的连续性条件得到了反射和透射波的幅值系数.分析了入射波通过裂纹后的透射、反射系数与激励频率和裂纹尺寸之间的关系.为基于振动功率流方法识别圆柱壳表面损伤提供了理论基础.     

Wave development on a thinning liquid film

Experimental results are presented for the growth of surface waves on a liquid film that thins as it flows under gravity over the surface of an upright circular cone. The characteristics of the mean film are calculated on the assumption of quasi-parallel flow, and the actual mean thickness found to relate very closely to that found on this basis. The development of the film was found to fall into three phases: the entry zone in which the velocity profile of the film becomes established where no waves are visible, a region of wave growth in which amplitude, wave speed, and wave length all grow, and a final region in which amplitude and wave speed decline as the film thins further although wave length continues to grow. An empirical relationship is presented which expresses the wave number at any point on the cone in terms of the flow rate and a parameter based on the local Reynolds and Weber numbers and cone angle. It was found that for a given flow rate the maximum wave amplitude was reached at a value of wave number of 0·048.     

Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer

The dispersive behavior of small amplitude waves propagating along a non-principal direction in a pre-stressed, compressible elastic layer is considered. One of the principal axes of stretch is normal to the elastic layer and the direction of propagation makes an angle θ with one of the in-plane principal axes. The dispersion relations which relate wave speed and wavenumber are obtained for both symmetric and anti-symmetric motions by formulating the incremental boundary value problem for a general strain energy function. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of the anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress and propagation angle, it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds, while other higher modes have an infinite phase speed. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the Rayleigh surface wave speed and the limiting wave speeds of the layer, respectively. Numerical results are presented for a Blatz–Ko material and the effect of the propagation angle is clearly illustrated.     

Thermoelastic damping in micro-beam resonators

Thermoelastic damping is recognized as a significant loss mechanism at room temperature in micro-scale beam resonators. In this paper, the governing equations of coupled thermoelastic problems are established based on the generalized thermoelastic theory with one relaxation time. The thermoelastic damping of micro-beam resonators is analyzed by using both the finite sine Fourier transformation method combined with Laplace transformation and the normal mode analysis. The vibration responses of deflection and thermal moment are obtained for the micro-beams with simply supported and isothermal boundary conditions. The vibration frequency is analyzed for three boundary condition cases, i.e., the clamped and isothermal, the simply supported and isothermal, and the simply supported and adiabatic. The analytic results show that the amplitude of deflection and thermal moment are attenuated and the vibration frequency is increased with thermoelastic coupling effect being considered. In addition, it can be found from both the analytic results and the numerical calculations that these properties are size-dependent. When the thickness of the micro-beam is larger than its characteristic size, the effect of thermoelastic damping weakens as the beam thickness increases. The size-effect induced by thermoelastic coupling would disappear when the thickness of the micro-beam is over a critical value that depends on the material properties and the boundary conditions.     

输液曲管平面内振动的波动方法研究

采用Flügge曲梁模拟弯曲管道,推导了管内流体的加速度,在总体轴线不可伸长假定的基础上建立了曲管平面内振动的动力学方程;采用波动方法,获得了曲管内振动波的传播和反射矩阵,提出了计算曲管平面内振动固有频率的数值方法。算例分析中,通过计算两端固定半圆形曲管的临界流速并与已有文献结果对比,验证了本文方法的正确性。最后,计算了两端固定半圆形曲管在四种不同流速下的前四阶固有频率,结果表明,管内流速的增大会降低管道的固有频率,当流速增大到某一特定值时,管道的一阶固有频率消失。     

Finite-amplitude shear horizontal waves propagating in a pre-stressed layer between two half-spaces

The propagation of finite-amplitude time-harmonic shear horizontal waves, in a pre-stressed compressible elastic layer of finite thickness embedded between two identical compressible elastic half-spaces, is investigated. This is accomplished by combining finite-amplitude linearly polarized inhomogeneous transverse plane wave solutions in the half-spaces and finite-amplitude linearly polarized unattenuated transverse plane wave solutions in the layer. The layer and half-spaces are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. The special case where the interfaces between the layer and the half-spaces are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the shear horizontal wave speed with the pre-stress and the propagation angle.     

Propagation of concentration/density disturbances in an inertially coupled two-phase dispersion

Geurst's equations are used to predict the speed of disturbance wave propagation in a mixture containing a compressible dispersed phase. Results are obtained for the case when there is no relative velocity ahead of the disturbance and are compared with Karplus' data for air-water mixtures. The changes in density, void fraction and the velocities of each phase across the wave are predicted.     

Free vibration analysis of thin rotating cylindrical shells using wave propagation approach

The wave propagation approach is extended to study the frequency characteristics of thin rotating cylindrical shells. Based on Sanders’ shell theory, the governing equations of motion, which take into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotation, are derived. And, the displacement field is expressed in the form of wave propagation associated with an axial wavenumber k _m and circumferential wavenumber n. Using the wavenumber of an equivalent beam with similar boundary conditions as the cylindrical shell, the axial wavenumber k _m is determined approximately. Then, the relation between the natural frequency with the axial wavenumber and circumferential wavenumber is established, and the traveling wave frequencies corresponding to a certain rotating speed are calculated numerically. To validate the results, comparisons are carried out with some available results of previous studies, and good agreements are observed. Finally, the relative errors induced by the approximation using the axial wavenumber of an equivalent beam are evaluated with respect to different circumferential wavenumbers, length-to-radius ratios as well as thickness-to-radius ratios, and the conditions under which the analysis presented in this paper will be accurate are discussed.     

非局部广义热弹性理论下半导体微结构中波的反射研究

论文基于非局部热弹性理论,研究了纳米半导体介质中波的反射问题。首先建立了在耦合的非局部弹性理论,波型热传导理论和等离子扩散理论下问题的控制方程;然后运用谐波法,得到耗散方程的解以及反射系数率的解析表达式;最后通过数值计算给出了硅纳米结构中相速度、群速度随非局部参数的变化,讨论了非局部参数、热电耦合参数以及热弹性耦合参数对反射系数率的影响。     

Dynamic analysis of thick short length FGM cylinders

In this paper a thick short length hollow cylinder made of functionally graded materials (FGMs) under internal impact loading is considered. The inner surface of the cylinder is pure ceramic, the outer surface is pure metal, and the material composition varies continuously along its thickness. Finite Element Method based on Rayleigh-Ritz energy formulation has been applied to study the propagation of elastic waves in FG thick hollow cylinders. The Newmark direct integration method is applied to solve the time dependent equations. The time histories of displacements, stresses, wave propagation in two directions and velocities of radial stress wave propagation for various values of volume fraction exponent have been investigated. Also by using fast Fourier transform, the first natural frequencies for FG cylinders with simply-simply and clamped-clamped ends conditions are illustrated. The model has been compared with result of a plane strain FG thick hollow cylinder which is subjected to an internal impact loading, and it shows very good agreement.     

Numerical simulation of loading edge cracks by edge impact using the extended finite element method

The extended finite element method is used to analyze a plate with two parallel edge cracks impacted by a cylindrical projectile. The influence of the impact speed, crack length,plate thickness and notch tip radius on the crack initiation and propagation is studied. Dynamics equations are solved by an implicit time integration scheme which is unconditionally stable. Very good agreement is achieved between numerical predictions and experimental results. The critical velocity of the crack initiation under different conditions is examined. The influence of the crack length is greater than that of the impact speed, plate thickness and notch tip radius.     

Numerical Simulation of the 3D Laminar Viscous Flow on a Horizontal-axis Wind Turbine Blade

The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines that rotate at a constant angular speed. The numerical calculation of the development of the three-dimensional boundary layer on the surface of the blades is carried out under laminar conditions and considering flow rotation, airfoil curvature and blade twist effects. The adopted geometry for the twisted blades is given by cambered thin blade sections conformed by circular are airfoils with constant chords. The blade is working under stationary conditions at a given tip speed ratio, so that an extensive laminar boundary layer without flow separation is expected. The boundary layer growth is determined on a non-orthogonal curvilinear coordinate system related to the geometry of the blade surface. Since the thickness of the boundary layer grows from the leading edge of the blade and also from the tip to the blade root, a domain transformation is proposed in order to solve the discretized equations in a regular computational 3D domain. The non-linear system of partial differential coupled equations that governs the boundary layer development is numerically solved applying a finite difference technique using the Krause zig-zag scheme. The resulting coupled equations of motion are linearized, leading to a tridiagonal system of equations that is iteratively solved for the velocity components inside the viscous layer applying the Thomas algorithm, procedure that allows the subsequent numerical determination of the shear stress distribution on the blade surface.     

Wavelet Analysis of the Evolution of a Solitary Wave in a Composite Material

The evolution of a solitary wave propagating through a microstructural material (composite) is studied on the basis of wavelet analysis. A specific feature of the solution technique proposed is the use of Mexican hat (MH) wavelets, which are elastic wavelets, i.e., they are solutions of the basic system of wave equations for an elastic material with a microstructure. The initial wave profile is also chosen in the form of the MH-wavelet. Primary attention is given to the relationship among the profile behavior, wave bottom length, and characteristic microstructure length. A computer analysis conducted demonstrates that the approach proposed allows us to detect the basic wave effects: splitting of the wave into two modes with different phase velocities, simultaneous propagation of both modes in the components of the composite, and strong dependence of the evolution rate on the characteristic lengths of the wave and microstructure