动柔度与特征向量导数

现有特征向量导数分析了“直接法”用于求解很多特征向量导数的问题时,显得计算效率过低,为解决这个问题,本文导出了一种过渡动柔度式,使得计算很多个特征向量的导数时,计算效率高于现有各种“直接法”。     

计算重根特征向量导数的消元法

本文提出了重根特征向量导数计算的消无法，它分为若干直接算法和一种迭代算法。这种方法概念简单、实施容易、精度良好。该方法可经简单移值用于非重根情况。     

任意非亏损矩阵特征灵敏度分析的模态展开法

把特征向量的各阶导数表示成所有模态的线性组合，并利用左模态与右模态间的双正交性，首先导出了任意非亏损矩阵的重特征值的一阶导数所满足的特征值问题，然后根据此特征值问题无、看重根的情况，再导出了异导重特征值和等导重特征值对应的可微特征向量、特征值和特征向量各阶导数的一般计算公式。算例显示了方法的正确性。     

A family of modal methods for computing eigenvector derivatives with repeated roots

A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgün's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods. The project supported by the National Natural Science Foundation of China     

Dynamic flight stability of a hovering model insect: lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.     

Improved modal truncation method for eigensensitivity analysis of asymmetric matrix with repeated eigenvalues

An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,, λrof the matrix satisfy |λ1| |λr| and |λs| |λs+1|(s r-1), then associated with any eigenvalue λi(i s), the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to |λi/λs+1|q+1, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,, λs. A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.     

Dynamic flight stability of a model dronefly in vertical flight

The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion.The major finding is as following.Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion.Upward flight of the insect is also unstable,and the instability increases as the upward flight speed increases.Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.     

任意非亏损系统特征灵敏度分析的直接摄动法

本文发展了一种任意非亏损系统特征灵敏度分析的二阶段摄动法，将未摄动的问题的解作为零阶近似，把摄动影响作为摄动后问题的高阶修正，经过严格的数学推导，得到了支配高阶修正量的完全方程组。本方法无损知道摄问题的全部特征向量，仅需知被摄模态的特征对。本方法可处理被摄问题具有重特征值，甚至具有等导重特征值这一高度退化极难处理的情况。算例显示了本方法的正确性。     

一种新的减基法中的采样方法及误差估计

针对减基法中求解精度受减基空间完备性影响的问题,提出了一种基于向量空间逼近原理的采样方法及相应的误差估计。该方法使每一步采样得到的特征向量与之前已得到的特征向量所张成的向量空间角度最大,从而保证了每步采样所对应的特征向量都具有最弱相关性,进而使最终得到的特征向量基空间更具完备性。并且由该方法产生了一种先验特征值误差界,...     

Stabilization control of a hovering model insect: lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability (passive stability),because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion.Controllability analysis shows that although inherently unstable,the lateral disturbance motion is controllable.By feeding back the state variables (i.e.lateral translation velocity,yaw rate,roll rate and roll angle,which can be measured by the sensory system of the insect) to produce anti-symmetrical changes in stroke amplitude and/or in angle of attack between the left and right wings,the motion can be stabilized,explaining why the drone flies can fly stably even if the flight is passively unstable.     

Stabilization control of a bumblebee in hovering and forward flight

Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability （passive stability）. But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle （which can be measured by the sensory system of the insect）, to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.     

考虑频率依赖性的涂层复合结构固有特性求解

粘弹性阻尼材料的力学特性参数会随着频率的变化而改变,即具有频率依赖性,因而传统的动力学建模及分析方法不能满足实际涂层结构优化设计的需要。在简要介绍粘弹性阻尼材料频率依赖性的基础上,本文提出用特征向量增值法来求解涂层复合结构的固有特性,并详细推导了特征向量增值法的求解原理。由此,提出了特征向量增值法的计算流程,包括计算无阻尼系统的固有特性,用Fox and Kapoor或者Nelson方法计算复特征向量增量;用Rayleigh熵法求解复特征值。最后,以涂敷粘弹性阻尼材料的钛基薄板为例,求解了该复合结构的固有特性,并与经典的模态应变能法进行了比较,证明了所提方法的正确性。     

First-order perturbation solution to the complex eigenvalues

The matrix perturbation method is extended to discrete linear nonconservative system with unsymmetrical matrices in this article. By introducing the concept of the adjoint complex eigenvector and by making use of the orthogonality relationship in the complex mode theory, the first-order perturbation solution to the complex eigenvalues is derived. Numerical example shows that this method is efficient and practicable.     

Imperfect bifurcations in an initially curved plate loaded by incompressible axial airflow

This research proposes a parametric method to design dynamic compensator for high-order quasi-linear systems. According to the solutions of high-order generalized Sylvester equations, the completely parametric expressions of both the left and right eigenvector matrices and dynamic compensator are established. Based on the proposed method, we transform the closed-loop system into a linear time-invariant system with the desired eigenstructure. Further, the synchronization problem on Genesio–Tesi system and Coullet system is put forward to prove that the parametric method is effective and feasible.

     

GPS/SINS系统空中对准姿态角误差可观测性研究

提出一种新的判断系统可观测性和可观测度的方法,详细分析了机体各种运动对系统姿态角误差可观测性和可观测度的影响,并把该方法应用于组合导航系统的可观测性和可观测度的研究中。该方法利用了误差状态的最小二乘估计均方误差阵的特征值和特征向量,能判断系统的可观测度,避免进行卡尔曼滤波计算求协方差阵。仿真结果表明该方法简单、快速、有效。     

粘弹性阻尼结构系统振动特性的迭代分析

含粘弹性阻尼材料结构系统的振动特性分析是相当复杂的,求解比较困难,本文给出了一种有效的迭代解法。文中首先定义了广义Rayleigh商,指出求广义Rayleigh商的驻值问题等价于原特征问题的求解;由近似估计得到的特征向量,广义Rayleigh商给出一个较好的特征值近似估计。据此构造了迭代方法,并成功地计算了一些例子。     

计算亏损系统模态灵敏度的逐层递推演算方法

对不具有完全特征向量系的线性振动亏损系统,在由广义模态理论建立的亏损系统广义模态 空间中,给出了亏损系统广义模态灵敏度分析算法,并推导出以逐层递推方式计算广义模态 展开式系数的简便、快速的演算公式. 给出的数值算例证明了此方法的正确性和有效性.     

Dynamic flight stability of a bumblebee in forward flight

The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.     

横观各向同性层状场地对环形简谐荷载的位移响应

本文采用横观各同性层状粘弹性模型拟半空间上之的层状场地,用阻尼器取代其下部的半空间以吸收振动能量。     

The application of pattern recognition techniques in fault diagnosis of machinery equipment

In this paper,the characteristics of vibration signal of machinery in different runningconditions are statistically analysed,and some moments of statistical distribution of signalsare selected as the eigenvector to condense the state information.Here,we divide the statesof machinery into two:‘good’and‘aulty’,and the pattern recognition techniques are usedto classify the running conditions of machinery.At the end of this paper,the authors presentsome test data,and from the results obtained,it’s verified that the eigenvector selected isreliable and sensible to faults.And the results also show the effectiveness of classificationrule.