循环双周期系统控制方程的解耦

证明了Ｕ变换方法可使具有循环双周期特性的运动方程组（代数或微分方程组）解耦，给出了解耦方程的基本形式，所得结果可广泛应用于循环双周期系统的静力与动力分析．

循环噪声作用下周期调制双稳系统的驻留时间分布函数

提出了一种计算循环噪声作用下周期调制双稳系统驻留时间分布函数的理论方法。基于具有分段逃逸速率的两态模型理论,建立粒子逃逸的瞬时速率方程,推导得出驻留时间分布函数的递归表达式。基于此,分别计算信号振幅与循环噪声强度比值较大和较小2种不同情形下驻留时间分布函数的解析表达式。并且,从理论和数值模拟两方面分别阐明了循环噪声对驻留时间分布函数结构的影响。研究结果表明:驻留时间分布函数呈现指数衰减且在循环滞后时间处出现骤然下降趋势,且随着噪声强度和相关强度的增大驻留时间分布函数衰减速度变快,说明循环噪声能够加速粒子在势阱间的跃迁。此外,在周期信号的调制下,驻留时间分布函数在信号半周期的奇数倍处出现一系列峰值,这预示着系统发生了随机共振现象。

双周期参数系统的受迫振动响应

谐波减速器在制造过程中,如果柔轮齿与刚轮齿引入了周节累积误差,则谐波减速器在动力传递中将出现双周期时变扭刚度波动,形成双周期参数振动问题.本文引入基于组合频率的二重三角级数,逼近双周期参数系统受迫振动,应用谐波平衡,得到不含时间变量的谐波系数递推式,形成三维矩阵代数方程;采用矩阵降维法,将三维矩阵代数方程转化为两维矩阵代数方程,实现响应谐波系数的求解.研究结果对双周期参数振动中响应预测问题研究和工程应用具有一定的理论指导意义.

双周期压电网络用于叶盘结构振动抑制的研究

以整体叶盘振动抑制为目的,利用压电材料在叶盘结构不同扇区形成异周期系统,并将与压电材料连接的外部电路并联或串联形成不同形式的网络,建立该机电耦合系统的动力学方程,分析其对叶盘结构动力学特性的影响效果。研究发现,双周期压电网络对叶盘结构的频率影响很小,在本文所研究的叶盘结构模型的参数变化范围内仅对频率转向区有轻微的影响,变化最大只有2%;但是双周期压电网络会对叶盘结构的模态振型产生很大的影响,会使原各阶单一节径振型变为多节径振型,节径种类数跟双周期数有关;压电网络还会把机械位移转化为电荷位移;同时压电网络中电阻元件的引入提高了系统的模态阻尼比。这些都会对叶盘结构的振动响应起到很好的抑制效果。最后,采用修正的模态置信因子M M AC对双周期压电网络系统进行了振动抑制特性的评估,结果表明,通过对结构系统双周期数的设计能有效提高振动抑制效果。

两方向具有循环双周期性的控制方程的解耦

证明了应用Ｕ变换方法可使在两个方向上具有循环双周期特性的系统控制方程组解耦，导出了解耦方程的基本形式，所得结果可广泛应用于循环双周期系统的静力与动力分析．

Doubly Periodic Propagating Wave Patterns of （2＋1）-Dimensional Maccari System

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.

Analytical Solution of Weak-Coupling Periodically Driven Two-Level System

We present an approximate analytical solution to periodically driven two-level system in the weak-coupling regime. The analytical solution is in good agreement with the exact numerical solution in resonance and near resonance cases when Ω 〈 0.3ωa with Ω and ωa denoting the Rabi and transition frequencies respectively.

Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio （SNR） in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time T in the deterministic force, and the delay time 8 in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that： （i） There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. （ii） SR can be realized by tuning the time delay T or 8 with fixed noise, i.e., delay-induced stochastic resonance （DSR） exists.

The fast rotation of companions of compact objects in close binary systems

We have performed Monte Carlo simulations of the rotation of single stars and companions of compact objects(The compact objects are white dwarfs(WDs) and neutron stars(NSs)) in close binaries.We present a comparison between the rotation of companions of compact objects and that of single stars.We find that the rotation of the companions of compact objects is on average faster than that of the single stars.According to the distribution of the orbital period and the rotation angular velocity,we find that the rotation of the companions of compact objects is mostly accelerated by stable mass transfer.Tidal forces of the compact object can also affect the rotation of companion.