复合隔振体系多目标优化研究

传统动力设备的隔振,往往仅着眼于设备本身的振动抑制,而将其连接基础视为绝对刚性,忽略其振动.考虑"设备-隔振器-薄板基础"为复合隔振体系,设备通过4点安置在薄板上;并基于机械四端连接特性,推导了力的传递率.随后,在固支薄板振动分析的基础上,引入功率流理论,提出了多目标优化策略:使多点安置的设备隔振体系输入薄板的峰值功率流最小;与此同时,使动力设备尽可能地趋于均匀振动,以降低设备振动损害.多目标粒子群优化算法具有参数设置少,收敛快,优化能力强等优点,且可基于Pareto支配获得最优解.该研究将设备隔振、薄板振动、功率流传递以及智能多目标优化技术结合,固支薄板振动理论作为切入点为优化策略创造了有利条件.多目标粒子群优化算法的应用亦为工程隔振及振动控制提供了新思路.     

基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题

主要考察弹性薄板在规则外力作用下的振动模型.在给定外力源项随时间变化模式的情况下,通过对薄板局部区域一段时间的振动位移观测数据,来反演外力大小的问题,也就是通常所谓的弹性薄板反源问题.给出了弹性薄板反源解的唯一性定理,并推导出板方程的基本解.取基本解方法和Tikhonov正则化方法的精髓,在简谐模式源项作用的情况下,构造了一套算法来反解源项.对Euler-Bernoulli杆和Kirchhoff-Love板的数值算例表明,无论源项是否光滑,测量是否带有误差,基本解方法都因其较好的计算效果,有着广泛的适用性.     

非局部因子和表面效应对微纳米材料振动特性的影响

基于非局部理论和表面效应模型,导出表面吸附物对微纳米材料的动力学方程,研究非局部因子和表面能对微纳米传感器振动特性的影响．结果显示,非局部因子、表面能、吸附物种类、附加刚度和基底种类对微纳米结构的振动特性有重要影响．     

矩形薄板弹性振动的一般解析解

本文建立了矩形薄板弹性横向自由振动位型函数微分方程的一般解,可以求解任意边界矩形薄板的振动问题.以四边自由矩形板为例求解了板的频率及其振型.     

导电薄板的磁弹性组合共振分析

基于Mexwell方程,给出了导电薄板的非线性磁弹性振动方程、电动力学方程和电磁力表达式.在此基础上,研究了横向磁场中梁式导电薄板的磁弹性组合共振问题,应用Galerkin法导出了相应的非线性振动微分方程组.利用多尺度法进行求解,得到了系统稳态运动下的幅频响应方程,分析了组合共振激发的条件.根据Liapunov近似稳定性理论,对稳态解的稳定性进行了分析,得到了稳定性的判定条件.通过数值计算,给出了一、二阶模态下共振振幅随调谐参数、激励幅值和磁场强度的变化规律曲线图,以及系统振动的时程响应图、相图、Poincare映射图和频谱图,进一步分析了电磁、机械等参量对解的稳定性及分岔特性的影响,并讨论了系统的倍周期和概周期等复杂动力学行为.     

偏心冲击荷载作用下薄圆板动力学响应的保结构分析

关注动力学系统的局部几何性质,采用多辛分析方法研究了偏心冲击荷载作用下薄圆板振动特性.在探索偏心冲击荷载作用下薄圆板振动问题动力学控制方程的对称性和守恒律的对应关系基础上,对动力学控制方程在多辛体系下重新描述,并采用显式中点差分离散方法构造其多辛格式,通过对存在不同相对偏心距冲击荷载作用下的薄圆板振动过程的数值模拟,研究了相对偏心距对薄圆板振动特性的影响,同时,数值模拟结果也充分体现了多辛算法的良好保结构性能.该研究结果不仅为由于荷载作用位置误差带来的动力学响应偏差估计提供了依据,而且为偏心冲击动力学问题的研究提供了新的途径.     

线载和弹性支承作用面内运动薄板磁固耦合双重共振

针对磁场环境中具有线载荷和弹性支承作用的面内运动薄板,给出了系统的势能、动能及电磁力表达式,应用Hamilton变分原理,推得面内运动条形板的磁固耦合非线性振动方程.考虑边界为夹支 铰支的约束条件,利用变量分离法和Galerkin积分法,得到了含简谐线载力和电磁阻尼力项的两自由度非线性振动微分方程组.应用多尺度法对主 内联合共振问题进行解析求解,得到了双重联合共振下系统的一阶状态方程和共振响应特征方程.通过算例,得到了面内运动薄板的一阶和二阶共振幅值变化规律曲线图,分析了不同作用量和载荷位置对系统振动特性的影响.结果表明:系统发生主 内双重共振时,解的多值性和跳跃现象明显,弹性支承和线载荷位置对共振现象影响显著;一阶和二阶的共振多值解区域同时出现同时消失,体现了明显的内共振特征.     

辛体系下碳纳米管阵列中太赫兹波传播特性研究

应用有效介质理论,研究了周期碳纳米管阵列中电磁波在太赫兹频段的传播特性.考虑碳纳米管阵列的非局部准静态模型,将其导入Hamilton系统的辛几何理论框架下,通过求解本征值问题得到了电磁波在碳纳米管阵列中传播的色散关系.数值计算结果给出了垂直和倾斜排列的碳纳米管阵列中电磁波传输特性.研究表明在太赫兹频段,轴向非局部空间色散对电磁波传播特性影响较小.相关研究可对太赫兹频段碳纳米管阵列波传播器件的设计提供理论参考.     

基于扭转模态的角振动压电俘能器研究

以线性压电理论为基础,分析了压电陶瓷圆柱壳的扭转振动问题.由于压电陶瓷柱壳的扭转振动使得覆盖于柱壳两端的电极之间出现电势差,通过导线连接两电极与外负载,则圆柱壳在振动过程中所捕获的能量能有效地供给微电子器件工作.得到了输出电压、电流、能量、效率以及输出功率密度的解析表达式,并数值分析了这类压电俘能器的基本性能.结果表明,这种结构能够用作压电俘能器,将旋转机械能转化成为电能.     

新型轻质复合材料夹芯结构振动阻尼性能研究进展

作为新一代先进轻质超强韧结构材料,复合材料格栅和点阵夹芯结构受到了国内外学者的广泛关注.目前关于该类结构材料的设计制备以及相关力学性能研究已取得了大量的研究成果.然而对该类结构振动阻尼性能的研究则处于起步阶段.该文综述了纤维增强树脂基复合材料简单层合结构以及各类夹芯结构振动阻尼性能的研究现状.首先阐述其阻尼机理, 然后分别概述了复合材料简单层合板的微观和宏观阻尼模型、复合材料粘弹性阻尼夹层结构和新型夹层结构的阻尼预报工作,最后总结归纳现有关于该类结构阻尼特性研究工作中已取得的成果和不足之处,并对其未来发展进行了展望.     

Multi-objective design optimization of an engine accessory drive system with a robustness analysis

Designing a good engine accessory drive system becomes a hard work with its increasingly complicated configuration and high demands on its dynamic characteristics. In this work, a hybrid mutation particle swarm optimization (HMPSO) algorithm is presented to optimize the key structure parameters of an engine accessory drive system for its vibration control. The superiority of the HMPSO algorithm against several other concerned metaheuristic algorithms in terms of solution quality and stability are verified by non-parametric statistical tests on ten benchmark functions. The design problem of the engine accessory drive system is a multi-objective optimization problem; the weighted sum method and main target method are applied to convert it to a single-objective one. Optimization on an example engine accessory drive system using the HMPSO algorithm demonstrates obvious improvement in system vibration after optimization. A robustness analysis is conducted to identify the robustness of dynamic responses of the engine accessory drive system with respect to small variations of the design variables relative to the optimal design in the design space, and suggestions on design of an engine accessory drive system are given according to it.     

Thermal alternation induced vibration analysis of spacecraft with lateral solar arrays in orbit

The rigid-flexible-thermal coupling dynamic analysis for a spacecraft in orbit is studied in this paper. The spacecraft consists of a central rigid platform and two groups of lateral solar arrays. There exists the relative motion between the rigid platform and solar arrays, thus the spacecraft is a multi-rigid-flexible bodies coupling system. As the spacecraft in orbit experience different light areas, alternations of the heat flux on solar arrays can result in changes of dynamic characteristics. Considering thermal stress effects of solar arrays, the dynamical model of the spacecraft is established by using Hamiltonian principle. Further, multi-rigid-flexible coupling modes of the system are obtained. The finite difference method is developed to obtained the responses of the spacecraft and the variation of temperature gradients under the different solar radiation. Results of natural characteristics illustrate that constrained modes can be used to discrete the system directly and efficiently. Modal shapes and parameters analysis reveal the rigid-flexible coupling effects of such spacecraft. The thermal-structural analysis demonstrates the thermal alternation may induce the vibration and even change the original vibration of the spacecraft.     

Modeling and analysis of distributed electromagnetic oscillators for broadband vibration attenuation and concurrent energy harvesting

Many energy harvesting devices employ dynamics ascribed to the classical vibration absorber. Conventional models suggest that when host structural motion excites the harvesters at resonance, maximum electrical power output is achieved. As the harvesters become inertially substantial relative to the structure, this condition no longer holds since the electro-elastic response of the harvester is coupled to the structural vibration. In this regime, the devices become true vibration absorbers that alter the structural oscillations which may consequently affect energy harvesting capability. Distributions of point oscillators have been considered as broadband vibration control treatments making it natural to consider the potential for energy harvesting devices to serve this end. This paper presents an analysis of distributed single- and two-degree-of-freedom, linear electromagnetic oscillators attached to a harmonically excited panel. The coupled Euler–Lagrange equations of motion are solved and the simultaneous goals of vibration attenuation of the host panel and harvested electrical power are computed for several scenarios. It is found that design parameters optimizing the individual goals occur in relative proximity such that small compromises need to be made in order to achieve both ends reasonably well, particularly in regards to the overall mass added to the structure.     

Nonlinear dynamics of high-dimensional models of in-plane and out-of-plane vibration in an axially moving viscoelastic beam

Nonlinear dynamics of high-dimensional models of an axially moving viscoelastic beam with in-plane and out-of-plane vibration with combined parametric and forcing excitations are investigated by the incremental harmonic balance (IHB) method in this paper. Governing equations of transverse in-plane and out-of-plane and longitudinal vibration are obtained basing on the Hamilton's principle. The Galerkin method is used to separate time variable and spatial variable to obtain a set of multi-order differential equations. The IHB method with the fast Fourier transform (FFT) is used to solve periodic response of high-dimensional models of the beam for which convergent mode is reached. Stability of the steady-state periodic solutions is analyzed using the multivariable Floquet theory. Particular attention is paid to in-plane and out-of-plane vibration on convergent mode of the beam with combined parametric and forcing excitations. Multiple solutions are observed, and jump phenomena between in-plane and out-of-plane vibration with different transverse cross sections are discovered.     

超越方程的优化解法

针对粒子群算法局部搜索能力差,后期收敛速度慢等缺点,提出了一种改进的粒子群算法,该算法是在粒子群算法后期加入拟牛顿方法,充分发挥了粒子群算法的全局搜索性和拟牛顿法的局部精细搜索性,从而克服了粒子群算法的不足,把超越方程转化为函数优化的问题,利用该算法求解,数值实验结果表明,算法有较高的收敛速度和求解精度。     

Theoretical Analysis of the Magnetic Cloaking Problem Based on an Optimization Method

Control problems are considered for a model of magnetic scattering on a permeable anisotropic obstacle shaped as a spherical layer. Such problems arise in developing technologies for designing magnetic cloaking devices when the corresponding inverse problems are solved by an optimization method. The solvability of the direct and extremal problems for the model in question is proved and the optimality system is derived. Its analysis permits obtaining sufficient conditions on the initial data which ensure the local uniqueness and stability of the optimal solutions.     

覆冰输电导线舞动的Noether对称性和守恒量

为克服传统输电导线非线性振动响应数值模拟的非保结构缺点,研究了输电导线在覆冰和大风激励条件下双向舞动中的Noether对称性和守恒量.首先,考虑空气动力和导线几何的非线性,依据分析力学方法建立了垂向与扭振两自由度舞动模型;其次,引进群分析理论,根据不变性原则给出了系统存在Noether对称性的条件以及相应守恒量的形式;最后,构造了一种保守恒量离散数值算法.研究表明,用Noether对称性理论研究机械结构非线性动力学系统力学特性,能保系统内在结构属性,方法新颖,适用范围广,结果可靠准确.     

具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型．优化过程由两级组成,拓扑级优化和形状级优化．在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索．对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响．     

Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.     

A method for determining control inputs for prescribed accelerations of the end-effector of a motion-simulator robot

Described in this paper is an approach for generating control inputs for an industrial Kuka robot such that it produces prescribed linear acceleration time histories for a given point of the end-effector. The method takes into account the workspace limits, and uses the internal interpolation cycle of the robot controller to generate the corresponding trajectories that will produce the prescribed accelerations. The PI parameters of the internal interpolation are identified from test measurements. The control scheme consists in producing time-varying values for the desired angle values of the interpolation algorithm, making the changes as the algorithm proceeds and thus generating smooth trajectories. The resulting acceleration of these trajectories is compared to the prescribed accelerations, and an optimization procedure is run such as to determine the required time-histories of the desired angles for the interpolation algorithm such that both accelerations match. The approach is demonstrated for the example of a 500kg payload Kuka robot that is aimed at producing given motions as a physical motion simulator (e. g. for cars or complex working machines). It is shown that the desired accelerations can be generated accurately and with high repeatability, making the approach suitable for example for simulating car rollover tests. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)