Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch

The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincaré mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincaré section also approves the previous conclusion.     

Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method

A perturbation-incremental (PI) method is presented for the computation, continuation and bifurcation analysis of limit cycle oscillations (LCO) of a two-degree-of-freedom aeroelastic system containing a freeplay structural nonlinearity. Both stable and unstable LCOs can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Thus, the present method is capable of detecting complex aeroelastic responses such as periodic motion with harmonics, period-doubling (PD), saddle-node bifurcation, Neimark-Sacker bifurcation and the coexistence of limit cycles. Emanating branch from a PD bifurcation can be constructed. This method can also be applied to any piecewise linear systems.     

Modeling of enhancement of nonlinearity in oxide and chalcogenide glasses by introduction of nanometals

In this Letter we extended T-matrix to calculate the nonlinear susceptibilities of a composite nonlinear host and guest medium, and then applied this model to calculate the nonlinear susceptibilities of oxide and chalcogenide glasses by introduction of nanometals. The results of the model is in good agreement with experimental ones.     

Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.     

X射线脉冲星累积轮廓建模及信号辨识

为减少X射线脉冲星信号辨识所需的观测时间, 提出一种基于轮廓光子分布统计量的辨识算法. 用该方法分析了观测数据按不同周期累积所获轮廓的光子分布差异, 按累积周期正确与否, 对轮廓进行分类建模. 基于两类轮廓模型, 研究了光子分布统计量的性质差异, 以此进行信号辨识. 利用罗西X射线时变探测器数据进行了辨识实验, 结果表明该算法有效地减少了辨识所需的观测时间, 且不存在误检问题.     

Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I

The nonlinear refraction of chlorophosphonazo I (CPA I) was investigated using the Z-scan technique with a pulse Nd:YAG laser and a cw HeNe laser as excitation sources. Positive and large nonlinear refractive index attributed to resonant electronic nonlinear effect was observed under pulse 532 nm excitation. Under cw HeNe 633 nm excitation, the origin of optical nonlinearity was discussed in term of laser heating effect. The experimental results show that CPA I will have potential applications in nonlinear optical devices.     

Modeling the combined effects of basilar membrane nonlinearity and roughness on stimulus frequency otoacoustic emission fine structure

A theoretical framework for describing the effects of nonlinear reflection on otoacoustic emission fine structure is presented. The following models of cochlear reflection are analyzed: weak nonlinearity, distributed roughness, and a combination of weak nonlinearity and distributed roughness. In particular, these models are examined in the context of stimulus frequency otoacoustic emissions (SFOAEs). In agreement with previous studies, it is concluded that only linear cochlear reflection can explain the underlying properties of cochlear fine structures. However, it is shown that nonlinearity can unexpectedly, in some cases, significantly modify the level and phase behaviors of the otoacoustic emission fine structure, and actually enhance the pattern of fine structures observed. The implications of these results on the stimulus level dependence of SFOAE fine structure are also explored.     

Modeling of processes for nonmonochromatic radiation in a ring interferometer with nonlinearity, delay, and diffusion

A generalized mathematical model is suggested and the method of slowly varying variables is used. It is shown that the approximation of large radiative losses in an interferometer is not equivalent to the single-pass approximation. It is suggested to construct bifurcation and instability charts for a clear understanding of the influence of physical factors on the dynamics. It is shown that the loss of monochromaticity significantly complicates the structure of these charts and reduces the regions of stable radiation passage. It is established that the radiation delay in the interferometer gives rise to the bifurcation of period doubling at a smaller nonlinearity parameter. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 29–35, February, 2000.     

交叉克尔非线性对二阶非线性诱导透明的影响

考虑耦合介质存在交叉克尔非线性的情形下,研究了交叉克尔效应对耦合双谐振腔中二阶非线性诱导透明的影响.首先给出了描述体系理论模型的哈密顿量,再通过对海森堡-朗之万方程进行线性化,得到了探测场的透射率,进而得出系统的吸收和色散关系.研究结果表明,在交叉克尔非线性强度较小时,可忽略其对诱导透明的影响;随着交叉克尔非线性强度的增大,诱导透明窗口宽度随之快速变窄.此外,吸收曲线中还出现了双吸收峰.进一步增强交叉克尔非线性,导致原本出现的诱导透明消失,并在新吸收峰处产生了新的诱导透明,新的诱导透明的吸收零点位置随着交叉克尔非线性增加而向左偏移.这些结果可能在不透明介质的窄窗口光传输和提高光学腔的性能方面提供一些参考.     

热声学的基本理论和非线性,Ⅰ热声学

热声关系很早就受到了科学家的注意,近年来在理论上和实际中都有了重大的发展.本文从声学家的角度看热声学的理论和实验的发展过程,和热声学的基本理论.     

Optical nonlinearity and bistability of CdS

Experimental data concerning the nonlinear optical behaviour of CdS are reported. At cryo-temperatures an increasing nonlinear absorption at the exciton resonance is observed, with the aid of which optical hysteresis is demonstrated. At room-temperature saturation of the band-edge absorption is found at intensities as low as 10 kW/cm². The switch-on time is determined to be smaller than 6 ps.     

Optical nonlinearity of CdS

The discovery and investigation of optically nonlinear behavior of CdS is reviewed. The development is described from nonlinear anti-Stokes excitation via the characterization of inelastic light scattering processes and the identification of high-density phenomena like biexciton creation, excitonic collisions, and electron-hole plasma generation towards very recent time-resolved gain, light-induced grating, and in particular optical bistability experiments. CdS is thus shown to allow for an extremely wide variety of different optically nonlinear processes and may be regarded as a model material for this field. Possible applications show up for several of the described phenomena.     

Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong nonlinear stiffness at its free end.     

Interaction of nonlinearity and polarization mode dispersion

The derivation of the coupled nonlinear Schrödinger equation and the Manakov-PMD equation is reviewed. It is shown that the usual scalar nonlinear Schrödinger equation can be derived from the Manakov-PMD equation when polarization mode dispersion is negligible and the signal is initially in a single polarization state as a function of time. Applications of the Manakov-PMD equation to studies of the interaction of the Kerr nonlinearity with polarization mode dispersion are then discussed.