悬臂梁参数辨识及PD控制器的设计

首先介绍了用一种实验方法辨识悬臂梁的参数,建立其数学模型。然后基于此模型,利用控制理论并结合Matlab仿真设计了PD控制器。在Matlab中对基于PD控制器的控制系统进行仿真,获得了很好的仿真结果。用实时仿真系统dSPACE实现仿真模型与硬件装置的连接,利用压电陶瓷作为传感器和驱动器,建立了实验系统。实验结果表明,建立的数学模型比较接近实际的悬臂梁对象,设计的PD控制器能较好地抑制悬臂梁的振动。     

柔性悬臂梁非线性非平面运动的多脉冲轨道分析

首先建立了柔性悬臂梁非线性非平面运动的偏微分方程;然后运用Galerkin和多尺度方法得到平均方程．并利用规范形理论进一步将方程化简;最后用能量相位法求出多脉冲跳跃的能量函数序列．Dynamics软件数值计算表明：在系统中确实存在着由多脉冲跳跃而导致的Smale马蹄型混沌．     

硅悬臂梁脉象传感器温度补偿

阐述了采用硅悬臂梁制造的脉象传感器结构、设计和温度补偿原理。实验结果表明:补偿后的传感器具有灵敏度高、稳定性好,线性度为1%FS(0~5 N),重复性为0.5%FS,灵敏度为50 mV/N。给出的温度补偿晶体管对该脉象传感器的灵敏度温度漂移补偿效果好,有推广应用前景。     

双晶悬臂梁式压电换能器建模与结构参数分析

针对如何提高悬臂梁压电发电效率的问题,通过对压电换能器进行力学分析并建立了一个电路等效模型,从而得到了悬臂梁谐振角振频率和输出功率的计算公式。通过代入数值进行计算仿真得出结构参数对输出功率的影响的曲线。通过分析得出:在设计悬臂梁的结构参数时尽量在结构强度允许的条件下选择更重的附加质量块,电极长度和梁的长度比值为0.8,压电陶瓷和金属层厚度比为0.25,能提高换能效率等结论。     

悬臂梁大变形的向量式有限元分析

为分析悬臂梁的几何非线性行为,用向量式有限元法将结构离散成质点系以及质点间的连接单元.根据牛顿第二定律得到每个质点在内力和外载荷作用下的运动方程以及悬臂梁在每个时刻的变形用该时刻质点系的运动表示.结合刚架元的节点内力和等效质量得出质点位移的迭代计算公式,采用FORTRAN编制计算程序,对悬臂梁分别承受集中载荷和弯矩下的大变形进行算例分析.计算结果与理论解吻合较好,表明该方法能很好地模拟分析悬臂梁的大变形.     

双晶压电悬臂梁俘能器的建模与仿真

针对双晶片悬臂梁式压电俘能器的优化问题,考虑悬臂梁末端位移与质量块质心位移的差异,对Roundy数学模型进行了修正.通过ANSYS有限元软件对俘能器建模并进行模态分析和谐响应分析,当质量块长度逐渐变大时,修正后数学模型对俘能器一阶固有频率和输出电压有更好的预测精度.研究了质量块形状和负载对俘能器输出特性的影响规律,发现在质量块质量不变时,提高质量块的质心高度能提高俘能器的发电能力,对俘能器的结构优化具有借鉴意义.     

一种高分辨力的光纤光栅悬臂梁动态解调技术

介绍了一种基于悬臂梁的匹配光栅测量和解调方案,在外界加速度作用下,一个光纤光栅受压,另一个光纤光栅受拉,使波长调谐的灵敏度增加了1倍。实验证明了该方法寓解调和温度补偿为一体的优越性,本解调方案的波长移动分辨力为0. 01pm,可实现高分辨力加速度测量。     

变速移动弹簧阻尼质量系统作用下梁的动态响应

为了分析移动载荷作用下梁的动态响应问题,建立了移动振动质量系统作用下梁的动力学模型,推导出带有附加矩阵和附加向量的时变动力学耦合方程,并整理成便于数值求解的二阶微分方程组,通过与移动力模型和移动质量模型的比较,验证了这一方法的可行性,在算例中比较了移动载荷不同运动情况下梁的挠度、弯矩和剪力动载系数.     

Optimality conditions for a nonconvex set-valued optimization problem

In this paper we study necessary and sufficient optimality conditions for a set-valued optimization problem. Convexity of the multifunction and the domain is not required. A definition of K-approximating multifunction is introduced. This multifunction is the differentiability notion applied to the problem. A characterization of weak minimizers is obtained for invex and generalized K-convexlike multifunctions using the Lagrange multiplier rule.     

可伸缩复合材料悬臂梁的非线性动力学建模及分析

首先,根据Reddy给出的考虑高阶剪切效应的层合理论,气动弹性活塞理论,利用Hamilton原理,对考虑采用基于活塞理论的一阶非线性气动力和面内参数激励的联合作用下的轴向可伸缩复合材料悬臂梁进行非线性动力学进行建模,得到其偏微分动力学控制方程.然后对控制方程无量纲化,利用Galerkin方法对控制方程进行了截断,得到三个可反映可伸缩悬臂梁横向振动的无量纲形式的常微分非线性动力学方程,只要选取适合的复合材料及其相关参数,使用数值方法就对模型在外伸和回收过程中的相关振动特性进行了分析.     

悬臂梁限位器非线性动力学效应实验分析

针对具有限位器的悬臂梁系统设计了一个实验装置,通过实验分析限位器对悬臂梁系统非线性动力学行为的影响规律,展示了跳跃、多稳态以及它们之间的转换等实验现象.本文还分析了限位器宽度和高度对悬臂梁非线性幅频响应的影响规律,同时揭示了限位器宽度和高度对悬臂梁与限位器接触的一般规律.在实验中还发现了随外激励频率的变化,系统的运动从周期变为混沌再到跳跃的现象,同时给出了时间历程图与频谱分析图,并解释了这种现象.本文的研究体现了非光滑系统的丰富的非线性动力学现象.     

Numerical solution of a calculus of variations problem using the feedforward neural network architecture

It is demonstrated, through theory and numerical example, how it is possible to construct directly and noniteratively a feedforward neural network to solve a calculus of variations problem. The method, using the piecewise linear and cubic sigmoid transfer functions, is linear in storage and processing time. The L₂ norm of the network approximation error decreases quadratically with the piecewise linear transfer function and quartically with the piecewise cubic sigmoid as the number of hidden layer neurons increases. The construction requires imposing certain constraints on the values of the input, bias, and output weights, and the attribution of certain roles to each of these parameters.

All results presented used the piecewise linear and cubic sigmoid transfer functions. However, the noniterative approach should also be applicable to the use of hyperbolic tangents and radial basis functions.     

悬臂梁式SAW加速度计的信号特征及测量方案

加速度计设计的传统思路是设法利用好阻尼使悬臂梁尽快进入稳定状态,实现加速度的准确测量.然而,由于阻尼问题的复杂性和时变性,实际声表面波(SAW)加速度计的悬臂梁在外施待测加速度的作用下,常常会出现短暂位移振荡,进而引起声表面波谐振器(SAWR)谐振频率的振荡变化.本文分析了悬臂梁式SAW加速度计在高敏感、欠阻尼工况下SAWR信号的动态特征,提出了一种实时性较强的待测加速度值测量方案,并对该测量方案进行了必要的误差分析.     

基于Bezier插值方法的作大范围旋转运动锥形悬臂梁动力学研究

研究了作大范围旋转运动高度和宽度均沿着梁长度方向变化的锥形悬臂梁动力学问题. 采用 Bezier插值方法对柔性梁的变形场进行描述,考虑柔性梁的纵向拉伸变形和横向弯曲变形,计入由于横向弯曲变形引起的纵向缩短,即非线性耦合项. 运用第二类拉格朗日方程推导出作旋转运动锥形梁的动力学方程,并编制了动力学仿真软件,对作旋转运动锥形梁的频率和动力学响应进行研究. 结果表明: 不同锥形梁截面的动力学响应和系统频率将有明显差异,因此对实际系统合理建模,将能得到更为精确的结果.     

精确求解一类动态规划问题的神经网络

根据一类动态规划问题（ＤＦＤＰ）的特点，提出一种能够精确求解此问题的神经网络（ＬＤＰＮＮ）。ＬＤＰＮＮ具有结构简单、易于硬件实现、求解速度快并且能够求得精确最优解等优点，特别适合于大规模动态规划问题的求解。在复杂系统的实时优化与控制等方面具有广阔的应用前景。     

Stabilisation of Timoshenko beam system with a tip payload under the unknown boundary external disturbances

This paper is concerned with the boundary stabilisation of a Timoshenko beam with a tip payload under the boundary external disturbances. Nonlinear feedback control laws are designed to reduce the effects of the external disturbances. Since the controlled system is nonlinear, the well posedness of the nonlinear closed-loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle. In addition, we show the exponential stability of the nonlinear controlled system using the Lyapunov direct method. In the end, the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls.     

导出变系数非线性动力学系统拉格朗日函数的两种方法

利用从运动微分方程出发和从第一积分出发导出拉格朗日函数的两种直接方法,构造变系数非线性动力学系统¨x+b(x)x~2+c(x)x=0的拉格朗日函数和c(x)=0特殊情况的拉格朗日函数族.另外,讨论了这种非保守系统广义能量守恒的物理意义.     

车身梁截面库组件的开发

采用组件技术研究开发了车身梁截面库系统,可对现有的车身截面形状进行采集、编辑和管理,可计算截面的结构性能参数,支持对截面的不同方式查询,支持截面形状优化,帮助车身设计者设计和确定符合结构性能要求的车身截面参数和形状。论文介绍了车身梁截面事例库的结构和功能,详细给出了截面参数计算和形状优化的实现方法,最后给出了通过截面形状优化提高车身结构性能的算例。     

Constrained Fractional Variational Problems of Variable Order

Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint. In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational problem subject to a holonomic constraint. We establish necessary optimality conditions in order to determine the minimizers of the fractional problems. The terminal point in the cost integral, as well as the terminal state, are considered to be free, and we obtain corresponding natural boundary conditions.      

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load. The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young’s modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant’s stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength. This work was presented at the 7th World Congress on Structural and Multidisciplinary Optimization (WCSMO-7), May 21–25, 2007, Seoul, Korea.