Nonlinear static characteristics of piezoelectric unimorph bending micro actuators

The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.

A study on the seismic behavior of a retrofitted building based on nonlinear static and dynamic analyses

This study describes the seismic performance of an existing five storey reinforced concrete building which represents the typical properties of low-rise non-ductile buildings in Turkey. The effectiveness of shear walls and the steel bracings in retrofitting the building was examined through nonlinear static and dynamic analyses. By using the nonlinear static analysis, retrofitted buildings seismic performances under lateral seismic load were compared with each other. Moreover, the performance points and response levels of the existing and retrofitting cases were determined by way of the capacity-spectrum method described in ATC-40 (1996). For the nonlinear dynamic analysis the records were selected to represent wide ranges of duration and frequency content. Considering the change in the stiffness and the energy dissipation capacities, the performance of the existing and retrofitted buildings were evaluated in terms of story drifts and damage states. It was found that each earthquake record exhibited its own peculiarities, dictated by frequency content, duration, sequence of peaks and their amplitude. The seismic performance of retrofitted buildings resulted in lower displacements and higher energy dissipation capacity depending mainly on the properties of the ground motions and the retrofitting strategies. Moreover, severe structural damage (irreparable or collapse) was observed for the existing building. However, buildings with retrofit alternatives exhibited lower damage levels changing from no damage to irreparable damage states.

Nonlinear Static and Dynamic Stiffness Characteristics of Support Hydraulic System of TBM

Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.

NONLINEAR FREE VIBRATION OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION UNDER THE STATIC LOADS

In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.

Static Electric-Spring and Nonlinear Oscillations

The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.

Nonlinear Oscillations of a Magneto Static Spring-Mass

The Duffing equation describes the oscillations of a damped nonlinear oscillator [1]. Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited e.g. oscillations of a theoretical weightless-spring. We propose generalizing the mathematical features of the Duffing equation by including in addition to the cubic term unlimited number of odd powers of coordinate-dependent terms. The proposed generalization describes a true mass-less magneto static-spring capable of performing highly non-linear oscillations. The equation describing the motion is a super non-linear ODE. Utilizing Mathematica [2] we solve the equation numerically displaying its time series. We investigate the impact of the proposed generalization on a handful of kinematic quantities. For a comprehensive understanding utilizing Mathematica animation we bring to life the non-linear oscillations.

Simplified Step-by-Step Nonlinear Static Program Investigating Equilibrium Conditions of Electrons in Atom and Ionization Energies: Case Study on Argon

For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arranged on the outer surface of nucleus. Then, by taking into account the nucleus-electron interaction (attractive and repulsive) and the mutual electron-electron repulsions, and by a simple step-by-step nonlinear static analysis program, all the electrons are found to equilibrate on the outer surface of the same sphere, which is concentric and larger than nucleus. In a second stage, starting from an equilibrium sphere of electrons, one of the electrons is subjected to gradual forced removal, radially and outwards with respect to nucleus. Within each removal step, the produced work increment is determined and the increments are summed. When no more significant attraction is exerted by nucleus to removed electron, the total work gives the Ionization Energy. After removing of single electron, the remaining electrons fall on a lower shell, that is, they equilibrate on the outer surface of a smaller concentric sphere. For nucleus-electron interaction, an L-J (Lennard-Jones) type curve, attractive and repulsive, is adopted. When the parameter of this curve is n > 1.0, the Ionization Energy exhibits an upper bound. As parameter n increases from 1.0 up to 2.0, the attractive potential of L-J curve is gradually weakened. The proposed model is applied on Argon. It is observed that, as the number of electrons increases, the radius of equilibrium sphere increases, too, whereas the attractive nucleus-electron potential is reduced;thus the Ionization Energy is reduced, too. Particularly, as the number of electrons and the radius of equilibrium sphere exceed some critical values, the above two last quantities exhibit abrupt falls. A regular polyhedron is revealed, which can accommodate Elements up to atomic number Z = 146, that is 28 more than Z = 118 of existing last Element, as guide for initial locations of electrons in the above first program.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids

This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.

落石被动柔性防护网非线性静力设计方法及验证

被动柔性防护网是一种常见的落石灾害防治措施。针对当前落石被动柔性防护网尚无适用的工程化设计方法的现状,以非线性计算过程中结构内能与设计防护能级相等作为加载完成的判别准则,建立了落石被动柔性防护网的非线性静力设计方法。基于LS-DYNA对250~5000 kJ共8种常用能级的被动柔性防护网开展非线性动力分析,明确了冲击力的分布范围及相对大小,形成了适用于不同能级落石被动柔性防护网非线性静力设计的荷载模式。为了有效模拟被动柔性防护网特殊的受力特征,开发了由索单元与受拉弹簧单元组成的非线性耗能单元用于耗能器模拟,开发了内部由多段索单元组成的滑移索单元用于滑移边界以及网环单元模拟。基于对网片冲击试验的反演和3500 kJ被动柔性防护网的设计及足尺冲击试验检验,验证了所提出的落石被动柔性防护网非线性静力设计方法的有效性。

大跨度上承式钢管混凝土拱桥受力性能分析

研究目的:为系统地掌握西北地区大温差、峡谷风、高震区共存的复杂建设条件下上承式钢管混凝土拱桥的力学性能,以一座净跨400 m的公路同类型拱桥为例,按照现行设计规范,采用统一模量法建立三维杆系有限元模型,对概率极限状态设计方法要求的静力性能、稳定性、动力特性、抗震性能的组合工况进行全面、系统地分析和计算,为同类型桥梁设计提供参考。研究结论:(1)温度效应大于汽车荷载效应,拱脚处横风效应突出;(2)双向偏压、偏拉组合受力为单弦杆控制设计状态,拱顶为桁式拱肋承载力的薄弱位置;(3)腹杆、横撑、平联等构件与弦杆构造匹配性较好时,承载力及疲劳性能等易满足受力需求;(4)温度、徐变预拱度比车道荷载大很多;(5)主拱圈在材料、几何、双重非线性下稳定性分别下降了5.5%、11.9%、17.1%;(6)振型相对密集、频率值较小,主振型为面外弯扭振动,具有多方向和多角度耦联性;(7)时程分析结果大于反应谱分析结果,但小于静力工况,拱桥抗震性能好;(8)上承式钢管混凝土拱桥在复杂建设条件下具有良好的受力性能。

低频大幅隔振器设计及实验

为了突破传统隔振器刚度和承载能力之间的矛盾,需要隔振器具有高的静态刚度,低动态刚度的特性.如今的准零刚度隔振器技术可以实现低频微幅隔振,但是对于大幅振动,隔振效果并不明显甚至失效,因此突破宽幅隔振成为隔振领域亟待解决的问题.为此,我们利用多稳态折纸通过并联装配的方式,构造具有宽幅零刚度区间的折纸型隔振器,以解决传统隔振器振动抑制幅值较低的问题.本文建立了宽零刚度隔振器模型,提出宽幅零刚度的设计方法,并通过动力学分析分析了模型的隔振效果.最后搭建试验样机,验证了理论的正确性.这种设计打破了传统准零刚度隔振器单点准零的设计准则,能够在一个大幅范围内保证稳定性,同时实现零刚度,极大拓宽了隔振器的适用范围.这种设计理念能够被用在新隔振材料设计和航空、船舶等大幅低频动态环境中.

输电直线杆塔风灾易损性的准静态分析方法

如何合理并高效地评估既有输电杆塔的抗风承载性能及安全裕度,对电网的风灾预测及运维管理具有重要的意义。该文提出一种考虑风向效应杆塔结构易损性评估的高效实用方法。首先基于风工程原理,采用准静态分析框架推导给出不同设计风速下的杆塔整体风荷载的极值概率分布;随后综合考虑输电塔结构参数的不确定性及初始缺陷,通过非线性静力推覆分析(nonlinear static pushover analysis,NSPA)考察杆塔结构的抗风承载能力性能及对应的破坏准则;进而依据随机抽样分析得到杆塔结构的抗风承载力的概率模型;最后采用极限状态函数计算不同风向角下的杆塔风灾易损性概率曲线。研究表明,基于首次超越概率理论可以方便得到准静态分析框架下的整体风效应概率分布;准静态的基底剪力响应不受结构非线性状态影响,可作为整体风荷载作用的评价指标;基于构件屈服破坏与整体破坏内在联系,可建立合理的轻微、严重和倒塌的破坏准则;风向角对杆塔的抗风承载性能和易损性均有着显著影响,杆塔在60°风向角下的易损概率最高。

一种适用于重点设防类高层单跨钢连廊的结构设计

为满足《建筑抗震设计规范》(GB 50011—2010)对单跨框架结构应用场合的条文规定和建筑使用功能要求,提出一种适用于重点设防类高层单跨连廊的结构体系:X向为两跨框架+桁架结构,Y向为框架-支撑结构。分别采用静力弹性分析和动力弹塑性分析对本连廊进行计算。结构静力弹性分析结果表明:施工模拟顺序对结构的内力影响较小,连廊在X向本质上是一个单层双跨框架结构。连廊性能化设计结果表明其能达到中震弹性、大震不屈服的性能目标。连廊的非线性屈曲分析和连续倒塌分析结果表明:桁架受压斜腹杆屈曲会引发结构整体失稳;桁架受压斜腹杆、框架角柱和框架边柱失效不会引发结构连续性倒塌。最后对连廊进行罕遇地震和极罕遇地震作用下的动力弹塑性分析,结果表明:结构受力性能良好,构件损伤控制在“中度破坏”以内,能够满足规范大震不倒的设计要求。

到达时间服从泊松分布的平行机队列的最优随机排序问题

论文考虑多个分布下,根据每类加工时间函数最小化目标函数的不同类别的随机排序问题。这个问题常出现在分布式系统、网络和应用程序方面。模型中,最优排序策略在每台机器上是一个简单的静态优先策略。在这种排序策略下,排序问题可以寻找到最佳路径矩阵。考虑一个非线性规划问题,证明了任何局部最优即为全局最优,大大简化了,优化问题的解决方案。在到达时间为泊松分布的情形下,论文提供了一个最佳的排序策略,能够最小化每类时间函数。对一般各种静态实例应用此方法,可得到简单的近似算法。

航天管路系统网套金属软管试验研究与数值计算

针对广泛应用于航天管路系统中的金属软管静力学特性,使用试验方法和有限元仿真方法对其进行研究。对软管进行了无内压和内压0.5 MPa状态下的轴向拉压刚度试验、横向弯曲刚度试验,试验结果表明,金属软管轴向拉压刚度、横向弯曲刚度具有非线性特性,且其力学特性与内压状态有关。根据软管中网套的非线性轴向力-位移关系,在有限元仿真软件中建立了一种基于非线性弹簧系统的等效模型。数值结果表明,该模型中的分配系数Ca取0.95时,仿真结果与试验结果一致性较好。该模型能够有效复现金属软管静力学变形的非线性特性,为进一步静动力学分析提供参考。

汽轮机数字电液调节系统静态特性研究

研究汽轮机数字电液调节系统(简称DEH)静态特性可以为机组的灵活、经济运行奠定基础。以某600MW机组为例,从机理建模的角度分析其DEH各个组成环节的静态特性,最终得到DEH的四象限图。研究表明:DEH四象限图中第一象限保持线性关系,是由传动放大机构和配汽机构两个非线性曲线叠加形成的;软件凸轮和机械凸轮装置在调节系统中位置的不同,是造成DEH与机械液压调节系统四象限图差异的主要原因。

基于等效静载荷法的挤压铝门槛梁非线性结构优化

针对侧面柱碰撞工况下的挤压铝门槛梁截面正向设计问题,分析了基于等效静载荷(ESL)原理的非线性优化技术和传统优化技术的优缺点。研究显示:概念设计阶段基于等效静载荷法的非线性拓扑优化技术相比传统的线性拓扑优化技术,能得到更加贴近碰撞安全结构变形策略要求的拓扑路径;详细设计阶段,基于等效静载荷法的非线性料厚优化技术,在优化效率和优化方案性能方面都优于传统的近似模型数值优化技术。

锂电池极片变形特性的非线性有限元分析

为了改善锂电池极片在烘干过程中出现变形的问题,以及利用热空气压力差使极片悬浮的变形问题,从锂电池极片的角度探索极片的变形规律,从根本上解决极片的干燥问题。采用非线性有限元方法研究极片的力学特性,着重了解极片在不同气压下的变形情况,并基于修正的拉格朗日描述系统推导出的三角形平面单元增量平衡方程分析几何非线性问题。在此基础上,分析了极片在类似简支梁状态下受到的外部压力及自身重力作用下的横向静变形情况。比较计算得出的变形数据与实验测得的具体数值,发现设计的计算方法得出的结果与实验数值接近,证明在极片静止变形中,使用力学特性方法研究极片的变形非常有效。研究结果可为设计锂电池的烘干设备提供科学合理的依据。

防渗墙刚度对大厚度黄土地区均质土坝除险加固效果的影响

目前少有防渗墙加固对坝体非线性静力特性的影响研究。为了研究混凝土防渗墙在黄土高原深厚覆盖层湿陷性黄土地区病险土石坝除险加固中的适用性,以巴家咀水库土石坝为工程背景,采用有限元方法研究了上游马道处增设防渗墙后坝体的变形、应力、坝体剪应力水平、施工期防渗墙应力变形、加固后防渗墙变形、加固后防渗墙应力等方面的静力特性。结果表明:无论增设塑性混凝土还是刚性混凝土防渗墙,大坝渗透稳定和坝坡稳定均能满足要求,但刚性混凝土刚度不宜过大,避免产生严重裂缝。研究结果可为类似工程提供参考。

用余能原理求解非线性静不定结构的支承反力

根据余能原理,结构的余能对任一外力的偏导数,等于外力作用点沿该力方向位移。由于非线性静不定结构支承处的支承反力方向位移为零或转角为零,可直接把结构的余能对外力求一阶偏导数来求支承反力,克服了有关文献采用广义变分原理求非线性静不定结构支承反力时,存在增加计算量的不足。算例分析表明,采用本方法计算的支承反力与相关文献结果一致,梁截面曲率正负号判定对支承反力计算有着较大的影响。