Periodic Response and Chaos in Nonlinear Systems with Parametric Excitation and Time Delay

In this paper, the periodic motions of a nonlinear system with quadratic,cubic, and parametrically excited stiffness terms and with time-delayterms are obtained by the incremental harmonic balance (IHB) method. Theelements of the Jacobian matrix and residue vector arising in the IHBformulation are derived in closed form. A mechanism model representingthe one-mode oscillation of beams and plates is considered as anexample. A path-following algorithm with an arc-length parametriccontinuation procedure is used to obtain the response diagrams. Thesystem also exhibits chaotic motion through a cascade of period-doublingbifurcations, which is characterized by phase planes, Poincaré sectionsand Lyapunov exponents. The interpolated cell mapping (ICM) procedure isused to obtain the initial condition map corresponding to multiplesteady-state solutions.     

斜拉索模态试验参数研究

试验模态分析是斜拉桥索力测试中广泛应用的方法。该方法的关键之一是采取合理的试验方案获取可靠的响应信号以识别出正确的索振动频率。本文通过试验,详细讨论了斜拉索模态测试中若干试验参数,如激振类型、激振位置、传感器位置以及频率分辨率对试验结果的影响;比较环境激励与锤击激励的效果,验证了环境激励的方法也可以准确识别索的频率;最后给出了较为合理的斜拉索模态试验方案,用该方案确定的索力与理论计算结果相差不超过 1. 5%。     

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.     

Chaos in the softening duffing system under multi-frequency periodic forces

The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincare map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The Melnikov‘s global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.     

Lyapunov exponent and stochastic stability of quasi-non-integrable Hamiltonian systems

An n degree-of-freedom (DOF) non-integrable Hamiltonian system subject to light damping and weak stochastic excitation is called quasi-non-integrable Hamiltonian system. In the present paper, the stochastic averaging of quasi-non-integrable Hamiltonian systems is briefly reviewed. A new norm in terms of the square root of Hamiltonian is introduced in the definitions of stochastic stability and Lyapunov exponent and the formulas for the Lyapunov exponent are derived from the averaged Itô equations of the Hamiltonian and of the square root of Hamiltonian. It is inferred that the Lyapunov exponent so obtained is the first approximation of the largest Lyapunov exponent of the original quasi-non-integrable Hamiltonian systems and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original systems can be obtained approximately by letting the Lyapunov exponent to be negative. This inference is confirmed by comparing the stability conditions obtained from negative Lyapunov exponent and by examining the sample behaviors of averaged Hamiltonian or the square root of averaged Hamiltonian at trivial boundary for two examples. It is also verified by the largest Lyapunov exponent obtained using small noise expansion for the second example.     

Parametric Excitation for Two Internally Resonant van der Pol Oscillators

The response of a system of two nonlinearly coupled van der Poloscillators to a principal parametric excitation in the presence ofone-to-one internal resonance is investigated. The asymptoticperturbation method is applied to derive the slow flow equationsgoverning the modulation of the amplitudes and the phases of the twooscillators. These equations are used to determine steady-stateresponses, corresponding to a periodic motion for the starting system(synchronisation), and parametric excitation-response andfrequency-response curves. Energy considerations are used to studyexistence and characteristics of limit cycles of the slow flowequations. A limit cycle corresponds to a two-period amplitude- andphase-modulated motion for the van der Pol oscillators. Two-periodmodulated motion is also possible for very low values of the parametricexcitation and an approximate analytic solution is constructed for thiscase. If the parametric excitation increases, the oscillation period ofthe modulations becomes infinite and an infinite-period bifurcationsoccur. Analytical results are checked with numerical simulations.     

Feedback minimization of first-passage failure of quasi non-integrable Hamiltonian systems

The non-linear stochastic optimal control of quasi non-integrable Hamiltonian systems for minimizing their first-passage failure is investigated. A controlled quasi non-integrable Hamiltonian system is reduced to an one-dimensional controlled diffusion process of averaged Hamiltonian by using the stochastic averaging method for quasi non-integrable Hamiltonian systems. The dynamical programming equations and their associated boundary and final time conditions for the problems of maximization of reliability and of maximization of mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The dynamical programming equations for maximum reliability problem and for maximum mean first-passage time problem are finalized and their relationships to the backward Kolmogorov equation for the reliability function and the Pontryagin equation for mean first-passage time, respectively, are pointed out. The boundary condition at zero Hamiltonian is discussed. Two examples are worked out to illustrate the application and effectiveness of the proposed procedure.     

Efficiency Improvement in Polymer Light‐Emitting Diodes by “Far‐Field” Effect of Gold Nanoparticles

The “far‐field” effect of metal nanoparticles (NPs), when chromophores localized nearby metal NPs (typically the distance >λ/10), is an important optical effect to enhance emission in photoluminescence. The far‐field effect originates mainly from the interaction between origin emission and mirror‐reflected emission, resulting in the increased irradiative rate of chromophores on the mirror‐type substrate. Here, the far‐field effect is used to improve emission efficiency of polymer light‐emitting diodes (PLEDs). A universal performance improvement is achieved for the full visible light (red, green, blue) PLEDs, utilizing gold (Au) NPs to modify the indium tin oxide (ITO) substrates; this is shown by experimental and theoretical simulation to mainly come from the far‐field effect. The optimized distance, between the NPs and chromophores with visible light emission ranging from 400 to 700 nm, is 80–120 nm. Thus the scope of the far‐field may overlap the light‐emitting profile very well to enhance the efficiency of optoelectronic devices. The 30–40% enhancement is obtained for different color‐emitting materials through distance optimization. The far‐field effect is demonstrated to enhance device performance for materials in the full‐visible spectral range, which extends the optoelectric applications of Au NPs.     

Plasmon Mechanism of Overdense Plasma Heating

This paper attempts to introduce an effective mechanism of plasma heating of an overdense plasma layer. This mechanism is directly related to the phenomena of anomalous transparency of an overdense plasma layer. High temperature is achieved due to the resonant excitation of the coupled surface waves on both sides of the plasma layer. The dissipative energy of the collisional effects appears as an effective heating source in this mechanism. The solutions of the heat equation under the resonant situations are obtained in the steady and unsteady states conditions. The main factors, affecting the considered plasma heating mechanism, are also discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于可调控多肽纳米管和石墨烯复合纳米结构的光吸收催化平台

近年来, 自组装纳米结构因为其容易制备、稳定、环保以及与各种功能基团、粒子等的多样结合能力吸引了科学家们的目光, 成为人们研究的热点课题, 在光电池、光催化、水凝胶、药物缓释等方面的实验科学领域得到了广泛的应用. 尤其是光催化方面, 自组装结构的重复性为激子的传递创造了比较良好的条件, 成为众多激子传递平台中的佼佼者. 本文报道了一种以苯丙氨酸二肽纳米管和羧基石墨烯为基础的自组装光吸收催化平台, 对其结构进行研究, 并使用该体系进行了烟酰胺腺嘌呤二核苷酸到它的还原态的催化实验. 该体系的微观结构由纳米管和石墨烯膜复合而成, 羧基石墨烯的存在能够降低纳米管直径, 实现纳米管的形态操控, 石墨烯与多肽纳米管复合纳米结构的存在实现了多通道协同激子传递, 降低了激子传递的距离, 极大增强了催化中心对于激子的接受和使用效率. 在复合了光敏剂和催化中心之后, 该体系具有较高的稳定性, 均一的分散性, 很强的光能吸收和转化能力等性质. 对于从NADP⁺往NADPH转变的催化实验表明, 该体系有较高的反应速率和催化效率, 并且比两种单一结构催化平台效果之和更好, 实现了一加一大于二的效应, 展现了复合纳米结构光吸收催化平台的巨大潜力和广阔应用前景.