求解一类非线性方程的改进的平均法

本文研究确定非线性方程一致有效近似解的平均法,得到B方法(Krylov-Bogoliubov method)与KBM方法(Krylov-Bogoliubov-Mitropolski method)的改进形式,通过两个例子与多尺度方法的比较,说明改进的平均法的有效性,从而拓广了平均法的应用范围。     

非线性能量汇胞元减振效率分析

非线性能量汇(nonlinear energy sink, NES)具有减振频带宽、减振效果好等诸多优点.但是NES没有线性刚度的特征导致其难以驱动大重量的NES振子,从而难以应用于对大型工程结构的减振.因此,将NES以高效和便捷的方式应用于工程减振,仍然是有待研究的问题.将NES以胞元的形式装配于振动的主结构中,通过多个NES胞元的共同作用,是一种有前景的减振策略.文章在偏心转子激励下,探究了多个NES胞元对远大于单个NES自身重量的振动结构的减振效果,分析了多个NES胞元耦合主结构组成的系统的整体响应特征.建立了NES胞元减振系统的运动微分方程,采用复化平均法(complexification-averaging,CxA)导出系统的慢不变流形及稳态响应满足的近似解析表达式,通过慢变流形的扰动运动微分方程对稳态解进行稳定性分析,再利用伪弧长法获得系统响应的近似解,分析了NES胞元的减振规律及系统响应规律,最后利用龙格-库塔(Runge-Kutta, R-K)法进行数值验证.结果表明,通过多个NES胞元共同作用,能够有效控制较大重量的主系统振动,而且减振效率随NES胞元个数和重量的增加...     

功能梯度简支矩形板的非线性动力响应

研究了功能梯度简支矩形板在横向简谐激励作用下的非线性动力响应问题。采用幂律分布规律描述功能梯度材料的等效材料参数,基于Galerkin法建立了系统广义坐标的常微分控制方程。利用平均法得到了系统的幅频响应特性,分析了功能梯度矩形薄板的非线性主共振特性。数值算例验证了平均化方法的正确性,揭示了功能梯度平板主共振响应中的多值性和跳跃现象;同时分析发现初始条件会改变功能梯度平板主共振的响应幅值。最后讨论了功能梯度材料的梯度指数对系统幅值响应的影响。     

多自由度Maxwell阻尼器减震结构(Ⅱ)——等效阻尼

对多自由度带支撑Maxwell阻尼器减震结构的等效阻尼比进行了系统研究。构建了耗能结构一般微分和积分混合地震响应方程组;基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析计算式。与一些典型问题的模态应变能法的计算精度进行对比分析,结果显示:本文方法的计算结果在特定条件下与精确解完全相同;在一个二自由度系统中相对位移响应方差的误差分别为0.99%和0.45%,优于应变能法的8%和5.4%,表明了本文方法的有效性。从而为建立此类耗能结构等效阻尼分析的完备解析解法、直接应用反应谱法进行实际工程设计提供了依据。     

用子波分析修正检测壁湍流猝发的VITA法

应用壁湍流脉动速度信号子波分析的一系列方法对检测壁湍流猝发事件的VITA法进行了修正。其中,用能量最大准则确定VITA法短时间平均周期;以子波变换能量最大尺度脉动速度的短时间平均方差的局部极大值点作为检测函数的中心点,取代了传统VITA法中对短时间周期平均方差选用门限值的方法,避免了VITA法检测结果对门限值的主观经验依赖性,提高了VITA法检测壁湍流猝发事件的客观性和准确性。     

Averaging analyses for spacecraft orbital motions around asteroids

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.     

Dynamics of a prey-predator system under Poisson white noise excitation

The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.     

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.     

一种改进的等效线性化方法

提出了一种改进的等效线性化方法.将现有方法中忽略的高阶谐波项作为等效线性方程的外激励,得到非齐次的等效线性化方程,利用谐波平衡法将该方程分解为一系列常微分方程组,用摄动法求解.算例表明,本文方法不仅提高了等效线性化方法的精度,而且对现有方法不能处理的含偶次非线性系统的分析同样有效.     

上海世博会气象馆平均风压数值模拟研究

采用数值模拟方法对上海世博会气象馆进行了平均风压数值模拟,比较了4种较适合于结构风工程的RNG k-ε,SST-k-ω,SSG-RSM和BSL-RSM湍流物理模型,包括体型系数、表面合力、合力矩及湍动能结果,同时结合风流动特性分析了其规律性和差别的原因,并得到SST-k-ω,BSL-RSM与SSG-RSM模型各有优势,而RNG k-ε模型稍差的结论.最后研究了有无干扰情况下的场馆表面平均风压系数,分析了风干扰的原因.