Wavelength-dependent Photodissociation Dynamics of Benzaldehyde

The ultrafast dynamics of benzaldehyde upon 260, 271, 284, and 287 nm excitations have been studied by femtosecond pinup-probe time-of-flight mass spectrometry. A bi-exponential decay component model was applied to fit the transient profiles of benzaldehyde ions and fragment ions. At the S2 origin, the first decay of the component was attributed to the internal conversion to the high vibrational levels of S1 state. Lifetimes of the first component decreased with increasing vibrational energy, due to the influence of high density of the vibrational levels. The second decay was assigned to the vibrational relaxation of the S1 whose lifetime was about 600 fs. Upon 287 nm excitation, the first decay became ultra-short （-56 fs） which was taken for the intersystem cross from S1 to T2, while the second decay component was attributed to the vibrational relaxation. The pump-probe transient of fragment was also studied with the different probe intensity at 284 nm pump.     

Crack-tip field on mode Ⅱ interface crack of double dissimilar orthotropic composite materials

Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.     

Interface crack problems for mode II of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.     

Adaptive control for autonomous rendezvous of spacecraft on elliptical orbit

A strategy for spacecraft autonomous rendezvous on an elliptical orbit in situation of no orbit information is developed. Lawden equation is used to describe relative motion of two spacecraft. Then an adaptive gain factor is introduced, and an adaptive control law for auton- omous rendezvous on the elliptical orbit is designed using Lyapunov approach. The relative motion is proved to be ultimately bounded under this control law, and the final relative position error can achieve the expected magnitude. Simulation results indicate that the adaptive control law can realize autonomous rendezvous on the elliptical orbit with relative state information only.     

边界元法计算切口多重应力奇性指数

提出采用边界元法直接计算V形切口的多重应力奇性指数。首先在切口尖端挖出一微小扇形域,在该域边界列常规边界积分方程,后将扇形域内的位移场和应力场表示成关于切口尖端距离ρ的渐近级数展开式,回代入切口边界积分方程,离散后得到关于切口奇性指数的代数特征方程,从而求解获得V形切口的应力奇性指数。该法避免了常规边界元法和有限元法在切口尖端附近布置细密单元的缺陷,并可同时求得多阶应力奇性指数。     

具有指数型弱耦合时滞系统的同步分支周期解

利用F loquet指数理论,研究了一类弱耦合时滞系统的参数在不同情况下同步分支周期解的稳定性。分别讨论了非耦合时滞系统分支周期解的存在性,稳定性及其近似表达式。通过实例利用MATLAB给出模型分支周期解的仿真图形,并分析了各参数对图形的影响。     

Vibrations of FGM thin cylindrical shells with exponential volume fraction law

In this paper, the influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells is studied. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love＇s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology.     

V形切口应力强度因子的一种边界元分析方法

将V形切口结构分成围绕切口尖端的小扇形和剩余结构两部分. 尖端处扇形域应力场表示成关于尖端距离$\rho$的渐近级数展开式,从线弹性理论方程推导出了一组分析平面V形切口奇异性的常微分方程特征值问题,通过求解特征方程,得到前若干个奇性指数和相应的特征向量. 再将切口尖端的位移和应力表示为有限个奇性阶和特征向量的组合. 然后用边界元法分析挖去小扇形后的剩余结构. 将位移和应力的线性组合与边界积分方程联立,求解获得切口根部区域的应力场、应力幅值系数和整体结构的位移和应力. 从而准确计算出平面V形切口的奇异应力场和应力强度因子.      

A Criterion for Stability of Synchronization and Application to Coupled Chua＇s Systems

We investigate synchronization in an array network of nearest-neighbor coupled chaotic oscillators. By using of the Lyapunov stability theory and matrix theory, a criterion for stability of complete synchronization is deduced. Meanwhile, an estimate of the critical coupling strength is obtained to ensure achieving chaos synchronization. As an example application, a model of coupled Chua＇s circuits with linearly bidirectional coupling is studied to verify the validity of the criterion.     

A new control law based on characteristic exponent assignment for libration point orbit maintenance

A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.