Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

The bending and free vibrational behaviors of functionally graded(FG)cylindrical beams with radially and axially varying material inhomogeneities are investigated.Based on a high-order cylindrical beam model,where the shear deformation and rotary inertia are both considered,the two coupled governing differential motion equations for the deflection and rotation are established.The analytical bending solutions for various boundary conditions are derived.In the vibrational analysis of FG cylindrical beams,the two governing equations are firstly changed to a single equation by means of an auxiliary function,and then the vibration mode is expanded into shifted Chebyshev polynomials.Numerical examples are given to investigate the effects of the material gradient indices on the deflections,the stress distributions,and the eigenfrequencies of the cylindrical beams,respectively.By comparing the obtained numerical results with those obtained by the three-dimensional(3D)elasticity theory and the Timoshenko beam theory,the effectiveness of the present approach is verified.

Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method

We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and Levison.The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.

Damage detection method in complicated beams with varying flexural stiffness

A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method （SSEM）, and its applicability condition is introduced. For a beam with the continuously varying fiexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.

Tunable optical gradient trap by radial varying polarization Bessel-Gauss beam

Optical tweezers play an important role in many domains, especially in life science. And optical gradient force is necessary for constructing optical tweezers. In this paper, the optical gradient force in the focal region of radial varying polarization Bessel- Gauss beam is investigated numerically by means of vector diffraction theory. Results show that the beam parameter and vary rate parameter that indicates the change speed of polarization rotation angle affect the optical gradient force pattern very considerably, and some novel force distributions may come into being, such as multiple force minimums, force ring, and force crust. Therefore, the focusing of radial varying polarization Bessel-Gauss beam can be used to construct optical traps.

基于密度锥削阵sin-FDA的波束方向图研究

频率分集阵列(Frequency Diverse Array, FDA)是作为一种全新的电扫描雷达体制,其方向图所具有的时间-距离-角度三维相关特性在电子对抗和安全通信等领域有广阔的应用前景。一维均匀线性FDA阵列(Uniform Linear Array Frequency Diverse Array, ULFDA)的发射方向图存在角度-距离耦合问题,针对这一问题,在对称子阵密度锥削阵结构的基础上,通过正弦频控函数取代原有的均匀线性函数,得到了FDA的点状波束指向控制方法。此外,针对FDA方向图的时变问题,得到了基于子阵结构的密度锥削阵sin-FDA主波束在角度维指向固定、距离维变化时的结论。

考虑齿圈柔性的内啮合齿轮时变啮合刚度计算分析

当前大多数内齿轮啮合刚度都是基于忽略齿圈基体变形的假设计算的,文中应用Weber能量法基于精确的齿廓曲线方程建立内齿轮悬臂梁等效模型,同时基于铁木辛柯(Timoshenko)曲梁理论计算齿圈基体的变形量,并将齿圈变形耦合到齿轮啮合刚度计算中。通过MATLAB GUI编程进行内啮合齿轮时变啮合刚度数值计算,分析了齿圈柔性对啮合变形的影响,研究了齿圈厚度、支撑数量及啮合力位置对啮合刚度的影响。结果表明:齿圈厚度和支撑数量的增加均有利于齿轮副啮合刚度的增大;啮合齿中线位于固定支撑点时,齿圈啮合刚度最大,在靠近支撑中间位置时,啮合刚度最小,齿圈啮合刚度对应于螺栓支撑呈周期性波动。

Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.

Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power;then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.

横纵向位移激励下变长度梁的动力学分析

关于变长度梁的研究,主要集中在横向自由振动及稳定性分析,有关水平及竖直两个输入方向的抗震研究却不够充分,常用的抗震设计方法没有充分考虑结构时变性对振动产生的影响。以实际工程中的变长度操作杆为算例,运用广义Hamilton原理建立横纵向地震激励下变长度梁的动力学方程,运用假设模态法与修正后的Galerkin法进行空间离散求解,通过数值仿真方法求解不同轴向运动下变长度梁在简谐波与地震波作用下的振动响应。根据计算结果,讨论了不同轴向运动所引发的梁长变化对变长度梁的振动影响规律。对比相同长度范围内变长度梁与固定梁在地震激励下的末端最大位移,前者在收缩时的结果大于后者。说明了在对变长度梁等时变结构进行抗震分析时,考虑结构时变性影响的必要性。该建模计算方法可为类似结构的抗震分析与设计提供参考。

PEC柱-型钢梁框架异型内节点的抗剪性能试验研究

由于民用建筑外观及工业建筑生产工艺要求,部分包覆钢-混凝土结构因错位、变梁变柱等会形成异型内节点.为研究该类异型内节点的抗剪性能,以柱两侧梁错位高度、单侧梁截面高度增大等为变量参数,按1∶2缩尺比例设计制作了1个常规内节点和3个异型内节点模型试件,并完成低周往复荷载试验,分析了内节点的破坏形态、滞回耗能、承载能力、延性性能等指标.试验研究结果表明:各试件滞回曲线均呈现对称饱满的梭形;等效黏滞阻尼系数在0.598~0.618,位移延性系数在3.28~4.96,表现出良好的耗能性能及变形性能;因错位、变梁形成的异型内节点与常规内节点相比,承载力分别提升约6.1%、14.0%、15.0%;位移延性系数提升了约-26.6%、11.0%、-14.1%,延性性能规律不明显,耗能能力、强度和刚度退化变化不大;对于左右梁截面尺寸相同且完全错开(即错位高度大于梁高)的Ⅰ类异型内节点,可按T形边节点进行设计;基于节点域传力机理,建立了Ⅱ类异型内节点抗剪计算模型,并提出了抗剪承载力计算公式,试验结果与理论计算结果吻合较好.

PULSATILE BLOOD FLOW THROUGH A VISCOELASTICITY-TETHERED TUBE OF MILD VARYING CROSS-SECTION

In this paper a mathematical model is developed for the description of the pulsatile blood flow through an axisymmetric artery of mild varying cross-section, taking into account the tethering effect of the sorrounding tissues.Based on the linear Navier-Stokes equation and boundary conditions,a set of differential equa- tions for the modulus of phase velocity,blood velocities,pressure and deformation of the vessel wall are deduced and the numerical solutions are found by utilizing the Runge-Kutta method.The axial velocity profiles and the peak wall shear stresses are given for both mild tapering tube and mild stenosed tube.It is shown that the peak wall shear stresses in the tethered tube are higher than those in the free tube.It is also shown that in a series of previously research work on peak wall shear stresses of varying cross-section vessels the free vessel assumption has the tendency of under assessing the peak wall shear stresses and vice versa for the rigid vessel assumption.

变速移动荷载作用下简支梁的动力响应分析

以变速移动荷载模拟车辆变速过桥,建立车轮加弹簧—阻尼器—簧上质量和均布质量2种变速移动荷载下欧拉梁的动力分析模型,并推导其运动控制方程。运用数值分析,研究简支梁在不同上桥初速度和加速度的匀变速移动荷载作用下的动力响应。结果表明:荷载以不同的加速度变速过桥时,桥梁的跨中挠度时程和动力放大系数曲线与匀速过桥时相似;变速移动荷载对桥梁动力响应的影响与荷载上桥初速度、加速度以及桥梁跨度等因素有关;移动车辆荷载使梁发生极大动力响应的上桥初速度出现在若干速度点上,是不连续的;跨中挠度不随移动荷载加速度的变化单调变化;简支梁跨度越大,变速移动荷载对跨中挠度的影响越大。

移动质量-简支梁系统的参数辨识

给出了移动质量 -简支梁系统的动力学方程 ,并用基于Hamilton原理的结构动响应算法对方程进行数值求解。然后介绍了一种新的从自由响应数据识别时变参数结构系统的伪模态参数的方法 ,并将该方法引入用于研究移动质量 -简支梁系统的参数辩识问题。

变截面箱梁剪力滞及剪切变形效应近似计算方法

变截面箱梁因其抗弯刚度沿梁轴向变化,通常采用有限元法分析,本文基于等效刚度及等效刚度比法,提出了一种可同时考虑剪力滞效应及剪切变形效应的,适用于手算的变截面箱梁荷载作用下挠度及剪滞系数的近似计算方法。通过一变截面悬臂箱梁算例分析,与初等梁理论计算结果进行了比较。结果表明:不考虑剪力滞效应及剪切变形效应将使得挠度计算结果偏小,对于此类箱梁截面而言,在计算挠度时,横向剪切变形效应的影响大于剪力滞效应的影响,而横向剪切变形效应对应力计算及剪力滞系数计算则无影响。本文方法使得解析计算理论能够方便地应用到工程实践中,为变截面箱梁的工程设计提供一种简单、有效的计算方法。

变截面梁柱刚度方程的Bessel函数解

本文提出一个计算 Bessel函数 Jp(x)及 Np(x)的近似方法并在 -∞ <p <∞和 x >0的范围内验证了方法的适用性 ,进而提出了截面按幂函数变化的变截面梁柱的刚度方程并研究了其临界力。

基于信号时频分析理论识别时变模态参数实验

为研究温度对结构模态参数的影响设计了一套温度可控的实验设备。在这套实验设备提供的可控温度环境中采集悬臂梁结构的加速度响应信号,利用基于信号时频分析的模态参数辨识算法处理实验数据,得到其时变模态参数,包括固有频率和振型,以此研究温度对其模态参数的影响。分析结果显示了基于信号时频分析的模态参数辨识算法在处理非平稳信号以得到结构的时变模态参数上的应用前景,更重要的是实验数据的分析结果较好地反映了温度对结构模态参数的影响,为热环境下结构振动特性分析提供了可靠而且有价值的分析方法和实验依据。

移动质量作用下轴向运动悬臂梁振动特性分析

将弹炮发射系统简化为移动质量作用下的轴向运动悬臂梁系统,推导了轴向运动梁的振动方程,采用修正的Galerkin法离散求解该偏微分方程,得到以模态坐标表示的二阶时变常微分方程组,通过Newmark-β法对方程组进行了求解。计算结果表明,移动质量载荷主要使梁的一阶模态受到激励,移动质量的大小和运动速度对悬臂梁的振动响应影响较大,在移动质量作用下梁的伸缩运动都处于不稳定状态;在移动质量脱离悬臂梁后,梁的轴向收缩运动使得梁的瞬时振动频率不断减小,振动位移逐渐衰减,而振动速度逐渐增大,梁的运动处于不稳定状态,伸展时梁的自由振动规律相反。

变速旋转梁的建模与运动稳定性分析

利用哈密顿原理建立了支承运动情况下变速旋转梁的弹性振动方程及边界条件 .根据模态分析方法 ,利用边界条件以及模态函数的性质 ,得到了一组惯性解耦时变系数的模态坐标方程组 .并分析了几种特殊情况下的经典时变振动方程即 Hill方程和 Mathieu方程 .将时变系数的常微分方程组变为增量形式 ,根据 Newmark方法逐步积分 ,运用梁端部弹性振动的相轨迹分析了该时变系统的稳定性 .最后给出了变角速度情况下 。

变高度悬臂箱梁剪力滞效应的半解析解

以等截面Euler梁的自由振动模态为Ritz基函数,提出了一种求解变高度箱梁剪力滞微分方程组的Ritz法。该方法首先进行与箱梁相同跨度相同边界条件等截面欧拉梁模态分析,然后将箱梁的竖向挠度和剪切转角用模态及其导数的线性组合来表达,从而将变分法所得箱梁剪力滞微分方程组转化为线性代数方程组进行求解。在此基础上,研究了参与计算模态阶数和截面高度变化率对计算误差的影响,算例分析结果表明:箱梁高度变化越大,Ritz法的收敛速度越慢;但随着参与计算模态阶数的增加,Ritz法将收敛到解析解。采用12阶以上模态进行计算,所得的剪力滞系数误差小于5%。