Transverse free vibration analysis of a tapered Timoshenko beam on visco-Pasternak foundations using the interpolating matrix method

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the eff ects of the Winkler coeffi cient, Pasternak coeffi cient and damping coeffi cient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary diff erential equations with variable coeffi cients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verifi ed through two numerical examples. The infl uences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with diff erent taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.

High-Power Single-Spatial-Mode GaSb Tapered Laser around 2.0 μm with Very Small Lateral Beam Divergence

We report high-power single-spatial-mode type-I GaSb-based tapered lasers fabricated on the InGaSb/AlGaAsSb material system. A straight ridge and three different tapered waveguide structures with varying flare angles are fabricated to optimize the output power and spatial-mode performance. The best devices exhibit single-spatial-mode operation with room-temperature output power up to 350？mW in continuous-wave mode at an emission wavelength around 2.0？μm with a very small far-field lateral divergence angle, which is beyond state of the art in terms of single-spatial-mode output power.

Flapwise Bending Vibration Analysis of Rotating Tapered Rayleigh Beams for the Application of Offshore Wind Turbine Blades

The flapwise bending vibrational equations of tapered Rayleigh beam are derived based on Hamilton’s principle.The corresponding vibrational characteristics of rotating tapered Rayleigh beams are investigated via variational iteration method(VIM).Natural frequencies and corresponding mode shapes are examined under various rotation speed,taper ratio and slenderness ratio focusing on two types of tapered beam.The convergence of VIM is examined as part of the paper.Validation of VIM solution is made by referring to results available in other literature and corresponding results show that VIM is capable of yielding precise results in a very efficient way.

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.

Bending of a Tapered Rod: Modern Application and Experimental Test of Elastica Theory

A tapered rod mounted at one end (base) and subject to a normal force at the other end (tip) is a fundamental structure of continuum mechanics that occurs widely at all size scales from radio towers to fishing rods to micro-electromechanical sensors. Although the bending of a uniform rod is well studied and gives rise to mathematical shapes described by elliptic integrals, no exact closed form solution to the nonlinear differential equations of static equilibrium is known for the deflection of a tapered rod. We report in this paper a comprehensive numerical analysis and experimental test of the exact theory of bending deformation of a tapered rod. Given the rod geometry and elastic modulus, the theory yields virtually all the geometric and physical features that an analyst, experimenter, or instrument designer might want as a function of impressed load, such as the exact curve of deformation (termed the elastica), maximum tip displacement, maximum tip deflection angle, distribution of curvature, and distribution of bending moment. Applied experimentally, the theory permits rapid estimation of the elastic modulus of a rod, which is not easily obtainable by other means. We have tested the theory by photographing the shapes of a set of flexible rods of different lengths and tapers subject to a range of impressed loads and using digital image analysis to extract the coordinates of the elastica curves. The extent of flexure in these experiments far exceeded the range of applicability of approximations that linearize the equations of equilibrium or neglect tapering of the rod. Agreement between the measured deflection curves and the exact theoretical predictions was excellent in all but several cases. In these exceptional cases, the nature of the anomalies provided important information regarding the deviation of the rods from an ideal Euler-Bernoulli cantilever, which thereby permitted us to model the deformation of the rods more accurately.

Lateral characteristics improvements of DBR laser diode with tapered Bragg grating

Broad area semiconductor laser(BAL)has poor lateral beam quality due to lateral mode competition,which limits its application as a high-power optical source.In this work,the distributed Bragg reflector laser diode with tapered grating(TDBR-LD)is studied.By changing the lateral width,the tapered grating increases the loss of high-order lateral modes,thus improving the lateral characteristics of the laser diode.The measuring results show that the TDBR-LD can achieve a single-lobe output under 0.9 A.In contrast to the straight distributed Bragg reflector laser diode(SDBR-LD),the lateral far field divergence of TDBR-LD is measured to be 5.23°at 1 A,representing a 17%decline.The linewidth of TDBR-LD is 0.4 nm at 0.2 A,which is reduced by nearly 43%in comparison with that of SDBR-LD.Meanwhile,both of the devices have a maximum output power value of approximate 470 mW.

Study on adhesively-bonded surface of tapered double cantilever specimen made of aluminum foam affected with shear force

Aluminum foam is widely used in diverse areas to minimize the weight and maximize the absorption of shock energy in lightweight structures and various bio-materials.It presents a number of advantages,such as low density,incombustibility,non-rigidity,excellent energy absorptivity,sound absorptivity and low heat conductivity.The aluminum foam with an air cell structure was placed under the TDCB Mode II tensile load by using Landmark equipment manufactured by MTS to examine the shear failure behavior.The angle of the tapered adhesively-bonded surfaces of specimens was designated as a variable,and three models were developed with the inclined angles differing from one another at 6°,8° and 10°.The specimens with the inclined angles of 6°,8° and 10° have the maximum reaction forces of 168 N,194 N when the forced displacements are 6,5 and 4.2 mm respectively.There are three specimens with the inclined angles of 10°,8° and 6° in the order of maximum reaction force.As the analysis result,the maximum equivalent stresses of 0.813 MPa and 0.895 MPa happened when the forced displacements of 6 mm and 5 mm proceeded at the models of 6° and 8°,respectively.A simulation was carried out on the basis of finite element method and the experimental design.The results of the experiment and the simulation analysis are shown not different from each other significantly.Thus,only a simulation could be confirmed to be performed in substitution of an experiment,which is costly and time-consuming in order to determine the shearing properties of materials made of aluminum foam with artificial data.

基于锥形掺镱光纤实现20 kW高光束质量激光输出

锥形光纤能够有效兼顾非线性效应抑制和模式控制,具备实现高功率、高光束质量光纤激光的潜力。近期国防科技大学研制了锥形掺镱光纤,采用1 018 nm光纤激光后向级联泵浦实现了20.2 kW激光输出,光束质量β因子平均值优于2,拉曼抑制比为33 dB。研究结果展示了锥形光纤在实现万瓦级高光束质量激光方面的优势。

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。

基于轨道控制的FEL圆偏振辐射的产生与空间分离

研究了在自由电子激光设施中产生高偏振度圆偏振辐射的技术方案。该方案将工作在反向渐变模式的平面波荡器和常规椭圆极化波荡器以前后连接的方式进行排布,并通过波荡器之间的矫正磁铁对电子束进行轨道控制。在平面波荡器部分利用偏转磁铁使电子束偏向传输,所产生线偏振辐射也将偏轴传播,脉冲能量为0.357μJ。在进入椭圆极化波荡器之前校正电子束的轨道和前进方向,使得带有微群聚结构的电子束沿轴线正向传输,其产生的圆偏振辐射能量为92.39μJ。圆偏振辐射将沿轴向传输,在一定距离后可实现其与线偏振辐射在空间上的分离。通过数值模拟分析了电子束偏转对辐射光性质所产生的影响。

脊锥比对锥形半导体激光器输出特性的影响

锥形半导体激光器是一种兼顾高功率高光束质量的光电子器件,但在高功率工作时易受非线性效应(如自聚焦和光丝)影响导致光束质量恶化。基于广角有限差分光束传播法(WA-FD-BPM)对总腔长为2500μm锥形半导体激光器进行模拟研究,分析了脊形区与锥形区长度比例对其输出特性的影响。结果表明,脊形区的滤波效应是影响锥形半导体激光器光束质量的重要因素,可通过合理优化脊锥比实现输出性能的提升。当脊锥比为2∶3时输出性能最佳。研究结果可为后续锥形半导体激光器的设计提供参考。

Analysis of wave propagation in micro/nanobeam-like structures: A size-dependent model

By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propaga- tion in micro/nanobeams is studied. The formulations of dis- persion relation are explicitly derived for both strain gradi- ent beam models, and presented for different material length scale parameters （MLSPs）. For both phenomenological size- dependent beam models, the angular frequency, phase veloc- ity and group velocity increase with increasing wave num- ber. However, the velocity ratios approach different values for different beam models, indicating an interesting behavior of the asymptotic velocity ratio. The present theory is also compared with the nonlocal continuum beam models.

Serviceability Analysis of Non-Prismatic Timber Beams: Derivation and Validation of New and Effective Straightforward Formulas

This paper provides innovative and effective instruments for the simplified analysis of serviceability limit states for pitched, kinked, and tapered GLT beams. Specifically, formulas for the evaluation of maximal horizontal and vertical displacements are derived from a recently-proposed Timoshenko-like non-prismatic beam model. Thereafter, the paper compares the proposed serviceability analysis formulas with other ones available in literature and with highly-refined 2D FE simulations in order to demonstrate the effectiveness of the proposed instruments. The proposed formulas lead to estimations that lie mainly on the conservative side and the errors are smaller than 10% (exceptionally up to 15%) in almost all of the cases of interest for practitioners. Conversely, the accuracy of the proposed formulas decreases for thick and highly-tapered beams since the beam model behind the proposed formulas cannot tackle local effects (like stress concentrations occurring at bearing and beam apex) that significantly influence the beam behavior for such geometries. Finally, the proposed formulas are more accurate than the ones available in literature since the latter ones often provide non-conservative estimations and errors greater than 20% (up to 120%).

FE Dynamic Analysis Using Moving Support Element on Multi-Span Beams Subjected to Support Motions

In the present study, finite element dynamic analysis or time history analysis of two-span beams subjected to asynchronous multi-support motions is carried out by using the moving support finite element. The elemental equation of the element is based on total displacements and is derived under the concept of the quasi-static displacement decomposition. The use of moving support element shows that the element is very simple and convenient to represent continuous beam moving, deforming and vibrating simultaneously due to support motions. The comparison between the numerical results and analytical solutions indicates that the FE result agrees with the analytical solution.

A New Synthesis Method for Sum and Difference Beam Pattern with Low Sidelobe

A new method for sum and difference beam pattern synthesis with low sidelobe is proposed.In the situation of phase taper weighting,it makes use of Fourier transform pair relationship existing between the array factor and the element excitations and uses a loop iterative way to derive the array element excitations according to given array factor.The iteration does not stop until the array element excitations meet the initial sidelobe requirements.The method overcomes the defects of traditional methods,such as more searching times,larger amount of calculation and poor robustness.In addition,it can also synthesize the low sidelobe pattern in case of element failures.Simulation verifies the effectiveness of the method.

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration.Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory,Bernoulli-Euler beam theory and D’Alembert’s principle together.A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables.The dimensionless deflection,amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration.Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough.Both frequency ratio and loading location are the important factors that determine the sizedependent performance of a micro-beams under forced vibration.

基于状态空间法的阶梯型变截面水平受荷桩分析方法

为研究阶梯型变截面桩的水平承载特性,基于Timoshenko梁理论,建立了综合考虑桩基尺寸效应、剪切变形和桩基材料非线性效应的四弹簧模型及其状态方程,获得了非线性桩土相互作用下任意长细比的桩截面内力与变形解析解。通过与已有文献中现场试验结果对比分析,验证该方法的适用性和有效性,并讨论了变径位置、桩径比和弹性模量比对桩基受荷特性的影响。研究结果表明:(1)桩基水平承载力对三者的敏感性为:桩径比>变径位置>弹性模量比;(2)综合考虑桩承载能力和经济性,建议变径位置、桩径比和弹性模量比取0.6。

Curve Optimization of Tapered Cantilever Beams Under Tip Loads

The study adopts the variational method for analyzing the cantilever tapered beams under a tip load as well as a definite end displacement,and further determining the optimized shapes and materials that can minimize the weights.Two types of beams are taken into account,i.e.,the Euler-Bernoulli beam without considering shear deformation and the Timoshenko beam with shear deformation.By using the energy theorem and the reference of isoperimetric problem,the width variation curves and the corresponding minimum masses are derived for both beam types.The optimized curve of beam width for the Euler-Bernoulli beam is found to be a linear function,but nonlinear for the Timoshenko beam.It is also found that the optimized curve in the Timoshenko beam case starts from non-zero at the tip end,but its tendency gradually approaches the one of the Euler-Bernoulli beam.The results indicate that with the increase of the Poisson’s ratio,the required minimum mass of the beam will increase no matter how the material changes,suggesting that the optimized mass for the case of Euler-Bernoulli beam is the lower boundary limit which the Timoshenko case cannot go beyond.Furthermore,the ratio r/E(density against Elastic Modulus)of the material should be as small as possible,while the ratio h2/L4 of the beam should be as large as possible in order to minimize the mass for the case of Euler-Bernoulli beam,of which the conclusion is extended to be applicable for the case of Timoshenko beam.In addition,the optimized curves for Euler-Bernoulli beam types are all found to be power functions of length for both tip point load cases and uniform load cases.

850nm高亮度锥形半导体激光器的光电特性

采用激射波长为850 nm的AlGaInAs/AlGaAs梯度折射率波导分别限制增益量子阱结构的外延片,设计并制备了具有条形结构和锥形结构的半导体激光器。在输出功率同为1 W时,锥形激光器的发散角、光束传播因子和亮度分别为4°、2.8和9.9 MW.cm-2.sr-1,远好于条形激光器的6°、9.2和3.0 MW.cm-2.sr-1。当外加3 A的脉冲电流时,锥形激光器峰值功率达到1.40 W,斜率效率为0.58 W/A,电光转换效率为30%。实验结果表明,锥形激光器可以在保证大功率输出的前提下,具有更高的光束质量。

基于样条有限点法的变截面Euler梁横向自由振动分析

基于Bernoulli-Euler梁理论,采用样条有限点法建立考虑截面高宽度沿轴线性变化的变截面Euler梁振动分析的计算模型,通过沿梁轴线设置一定数量的样条节点对变截面梁样条离散化,采用三次B样条函数对梁的位移场进行插值,基于Hamilton原理导出变截面Euler梁的振动方程,推导考虑截面尺寸变化效应的总刚度和总质量矩阵的表达式,并编制计算程序,算例分析表明,模型的变截面梁的横向自振频率解答与文献解答吻合良好,计算精度和计算效率高,且模型边界处理简单,取样条离散节点数为15时,模型可以取得较高精度且解答趋于稳定。模型可适用于不同边界、不同截面变化率和不同截面类型的变截面Euler梁的自由振动分析。