Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

Measuring supersymmetry at the large hadron collider

The large hadron collider (LHC) should have the ability to detect supersymmetric particles if low-energy supersymmetry solves the hierarchy problem. Studies of the LHC detection reach, and the ability to measure properties of supersymmetric particles are currently underway. We highlight some of these, such as the reach in minimal supergravity space and correlation with a fine-tuning parameter, precision measurements of edge variables, anomaly or gauge-mediated supersymmetry breaking. Supersymmetry with baryon-number violation seems at first glance more difficult to detect, but proves to be possible by using leptons from cascade decays.     

Mode competition in acousto-optically Q-switched planar waveguide lasers

Multi-mode rate equations have been developed to investigate mode competition in high-power acousto-optically Q-switched planar waveguide lasers. The mode competition arises from coupling effects and temporal losses in the transform between guided modes and free-space propagation. Pulse-to-pulse instability and temporal beam distortions are enlarged by mode competition when the laser works in the multi-mode regime. The influence of parasitic oscillation is also discussed. A Nd:YAG planar waveguide laser has been established with a folded hybrid/unstable resonator. A maximum average power of 83 W with a beam propagation factor is obtained. The theoretical simulation agrees well with the experimental observation.     

相位失配弹性平板复合波导中的缺陷态*

为了在弹性波波导中实现缺陷态的调控,该文基于相位失配原理设计了一种周期性平板波导结构。以正弦边界弹性波导为例,通过连接具有不同相位的两段波导结构,形成了弹性板中不同程度的缺陷,并分析了其谱带特性和能量局域化特征。结果表明,禁带中存在两个不同模式的缺陷态,其以透射峰形式出现并随着相位的改变产生频移。与此同时,两个缺陷态在空间上对应的应力场和位移场分布也具有不同的模态特征。该文提出的复合弹性波导缺陷态调控方法,不仅为研究弹性波与结构之间的内在联系提供了关键的理论支持,也为实际弹性波探测器件的设计提供重要参考。     

Mode III fracture analysis by Trefftz boundary element method

This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems. The project supported by the National Natural Science Foundation of China(10472082). The English text was polished by Keren Wang.     

Thermal buckling and post-buckling of pinned–fixed Euler–Bernoulli beams on an elastic foundation

In this article, both thermal buckling and post-buckling of pinned–fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically non-linear theory for Euler–Bernoulli beams, considering both linear and non-linear elastic foundation effects, governing equations for large static deformations of the beam subjected to uniform temperature rise are derived. Due to the large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the non-linear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second, and the third buckling mode shapes are plotted. From the numerical results it can be found that the buckling load-elastic foundation stiffness curves have no intersection when the value of linear foundation stiffness parameter is less than 3000, which is different from the behaviors of symmetrically supported (pinned–pinned and fixed–fixed) beams. As we expect that the non-linear foundation stiffness parameter has no sharp influence on the critical buckling temperature and it has a slight effect on the post-buckling temperature compared with the linear one.     

硅微机械谐振陀螺仪的非线性分析

给出了硅微机械谐振陀螺仪的结构,介绍了硅微机械谐振陀螺仪的工作原理,详细推导并给出了陀螺仪的输出频率和标度因数非线性的计算公式;基于影响谐振陀螺仪标度因数的参数,分析了由谐振器的振幅和梳齿静电驱动力引起的硅微机械谐振陀螺仪的非线性特性,给出了振动幅度与谐振频率关系的表达式.实验结果表明,陀螺仪的整体性能主要取决于谐振器振动幅度的稳定性.     

Interface crack between two shear deformable elastic layers

An improved method based on the first-order shear deformable plate theory is developed to calculate the energy release rate and stress intensity factor for a crack at the interface of a bi-layer structure. By modeling the uncracked region of the structure as two separate Reissner-Mindlin plates bonded perfectly along the interface, this method is able not only to take into account the shear deformation in the cracked region, but also to capture the shear deformation in the uncracked region of the structure. A closed form solution of energy release rate and mode decomposition at the interface crack is obtained for a general loading condition, and it indicates that the energy release rate and stress intensity factor are determined by two independent loading parameters. Compared to the approach based on the classical plate theory, the proposed method provides a more accurate prediction of energy release rate as well as mode decomposition. The computational procedures introduced are relatively straightforward, and the closed form solution can be used to predict crack growth along the layered structures.     

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

基于MgO:QPLN的多光参量振荡器电场调谐特性理论与实验研究

报道了基于掺氧化镁准周期极化铌酸锂(MgO:QPLN)的多光参量振荡器电场调谐特性理论与实验研究. 通过对电场调谐能力与极化结构参数间关联性的理论分析, 确定了高正负晶畴比MgO:QPLN电场调谐的可行性, 并模拟得到跨周期参量光输出波长与加载电压的关系曲线. 实验中通过对MgO:QPLN有效的电场加载, 实现了3.84 μm波段参量光的电场调谐, 频谱调谐带宽约6 nm, 调谐速率接近1 nm/kV, 进一步结合温度调谐, 实现了参量光宽谱段高精度的连续调谐. 所获得实验结果与理论模拟结果基本符合, 电场调谐在精度控制、快速响应方面相比于传统温度调谐更具技术优势.