Structural health monitoring based on sensitivity vector fields and attractor morphing

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.     

Analysis of a controlled chaotic autooscillatory system based on an anharmonic oscillator model

The mathematical model of a new autooscillatory system with chaotic dynamics based on self-excitation of an anharmonic oscillator is considered. The results of numerical analysis show the possibility of generating chaotic oscillations with linear gain in the delayed feedback and controlling chaos by means of parametric self-action.     

Synchronization of spin-transfer nanooscillator using phase-locking loop

It is suggested to use the phase locking (PL) principle for solving problems of synchronization and coherent power addition for spin-transfer microwave nanooscillators employing the phenomenon of magnetization oscillations in the microwave range excited by a spin-polarized current. The dynamics of a model spin-transfer oscillator with an inertial PL loop is considered. The regions of parameters corresponding to various dynamic regimes (synchronous, quasi- synchronous, beats) have been determined using bifurcation analysis. It is shown that the band of existence of synchronous regimes for a spin-transfer nanooscillator with a PL loop increases as compared to the analogous system synchronized by an external field.     

Improved heterodyne mixing efficiency and signal-to-noise ratio with an array of hexagonal detectors

An array of hexagonal pixel geometries is considered and its improvement in the mixing efficiency as well as the signal-to-noise ratio is compared with an equal-area array of square pixel detectors. We also consider the phase-front misalignment between the signal and the local oscillator wave fronts for both pixel geometries.     

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.     

Simulation modeling of the experimental parameter determination for a deteriorating vibrational system

Simulation is considered for the data-acquisition process on the behavior of a mechanical oscillator in which the elastic element is subject to degradation. An analysis and a comparison are presented for the forward and inverse treatments. An algorithm has been devised for the dependence on time of the damping coefficient and natural frequency as determined from the behavior curve for an ageing vibrational system. Translated from Izmeritel’naya Tekhnika, No. 10, pp. 5–8, October, 2008.     

Optical Lindblad operator in non-equilibrium thermo field dynamics

The Lindblad operator of the Markovian quantum master equation for an oscillator system is diagonalized by means of linear transformations of annihilation and creation operators in non-equilibrium thermo field dynamics. When the linear attenuation and amplification processes are considered, the left and right eigenstates of the Lindblad operator are constructed in terms of the transformed operators. In the linear attenuation process, the results are compared with those obtained by the damping base of the Lindblad superoperator. The base describing the time-evolution of the linear amplification process is derived and compared with the damping base. The method for diagonalizing the Lindblad operator is useful for calculating average values of physical quantities in the quantum Markovian process.     

Survival probability of nonlinear oscillators endowed with fractional derivative element and subjected to evolutionary excitation: A stochastic averaging treatment with path integral concepts

An analytical method for determining stochastic response and survival probability of nonlinear oscillators endowed with fractional element and subjected to evolutionary excitation is developed in this paper. This is achieved by the variational formulation of the recently developed analytical Wiener path integral (WPI) technique. Specifically, the stochastic average/linearization treatment of the fractional-order non-linear equation of motion yields an equivalent linear time-varying substitute with integer-order derivative. Next, relying on the path integral technique, a closed-form analytical approximation of the response joint transition probability density function (PDF) for small intervals is obtained. Further, a combination of the derived joint transition PDF and the discrete version of Chapman–Kolmogorov (C–K) equation, leads to analytical solution of the non-stationary response and survival probability of non-linear oscillator under the evolutionary excitation. Finally, pertinent numerical examples, including a hardening Duffing and a bi-linear hysteretic oscillator, are considered to demonstrate the reliability of the proposed technique.     

单驱动源混沌测量方法

混沌运动的基本特征表现为对初值的敏感依赖性。利用混沌轨道随初值的变化 ,定义了轨道距离 ,通过测量混沌轨道的距离测得该初始值。但混沌系统也同样对干扰极度敏感 ,初值相同的轨道由于电路中的噪声会指数分离 ,从而又完全否定了混沌系统可应用于小信号的测量 ,问题的关键是怎样降低电路的噪声。提出了一种新的混沌测量方法 ,与已有的混沌测量电路相比 ,该方法采用一个压控恒流源向混沌振子提供充放电电流。实验结果表明 ,它能改善测量系统的线性度和稳定性     

基于分形和子波变换自适应控制混沌

在自适应控制混沌方法的基础上结合子波分析、分形理论，提出了一种自适应控制受迫Ｄｕｆｉｎｇ振子的混沌运动的方法。克服了需要预先知道系统的具体动力学模型及需要设计一个参考模型等缺陷。从实验中即可测得系统的某个输出量，引入外力控制混沌运动。数值分析表明在适当的控制信号下，混沌运动得到了很好的控制。     

A new type of one-dimensional discrete map

A one-dimensional two-parameter map whose behavior on the plane of control parameters qualitatively reproduces the dynamics of a flow system — an rf oscillator describable by a system of three ordinary differential equations. It is it is shown that that the behavior of the map largely coincides with that of the flow system and is also similar to the results of a previous experiment on the rf oscillator. Pis’ma Zh. Tekh. Fiz. 24, 1–8 (September 17, 1998)     

High-power narrow-band pulses with wavelengths tunable about 1.053 µm from a synchronously pumped optical parametric oscillator

We have constructed an optical parametric oscillator to generate 75-ps near-transform-limited pulses with wavelengths tunable about 1.053 μm for use in pump-probe studies of self-focusing. The singly resonant oscillator uses a Brewster-cut LiB(3)O(5) crystal that is oriented for type-II phase matching and synchronously pumped by the amplified and frequency-tripled pulse trains from a mode-locked and Q-switched Nd:YLP laser. An intracavity Pockels cell is used to switch out single 0.5-MW pulses at rates of 1 to 10 Hz. The design, construction, and performance of the oscillator are discussed. Measured performance is compared with design predictions and with detailed numerical simulations.     

Modeling a transducer based on an optoelectronic oscillator for precision measurements of the optico-physical parameters of different media

A complete model of the operation of an optoelectronic oscillator functioning in the HF and UHF ranges in transient and steady-state modes is proposed and investigated by means of the method of slowly varying amplitudes. The efficiency gained with the use of this type of oscillator for the measurement of the opticophysical parameters of different media is considered using as an example an application of the oscillator for the determination of the length and index of refraction of an integral waveguide.     

Solution of the Master Equation for an Attenuated or Amplified Nonlinear Oscillator with an Arbitrary Initial Condition

Abstract

Using the thermo-field dynamics notation, an elegant solution of the master equation for an attenuated or amplified nonlinear oscillator is presented. It is found that, in this notation, the solution of the master equation under consideration amounts to a simple modification of that for the linear oscillator.     

New phase-noise model for crystal oscillators: application to the Clapp oscillator

Leeson's is the basic model for predicting oscillator noise. A mathematical analysis of this "heuristic" model has been proposed. Both models do not detail the relative importance of the amplifier transfer function associated to its own noise with regard to that of the resonator. In this paper, an improved version of those previous models is presented. The phase noise generated by the amplifier and the one generated by the resonator are differentiated without considering their origins, such as the conversion of amplitude modulation noise into phase modulation noise. The power spectral densities of phase noise at various points of the oscillator loop are calculated from their respective correlation functions. As a consequence, the influence of the inner amplifier and resonator noises on the resulting oscillator noise is predictable. The model is especially attractive to the makers of widely used quartz oscillators. The resulting oscillator noise is easily obtained from the oscillator open-loop noise. An example of the phase-noise modeling of the Clapp quartz crystal oscillator is simulated and discussed.     

Dynamics of a nonlinear oscillator under quasi-periodic drive action

The dynamics of a nonlinear oscillator under quasi-periodic drive action is studied using the model of an excitable electric circuit with a nonlinear diode. In the space (plane) of control parameters, the system dynamics is described by the torus doubling lines and the lines of transition to a strange nonchaotic attractor, which connect the so-called torus doubling terminal points. The transition to chaos in this system proceeds either via the formation of a strange nonchaotic attractor or via a torus-to-chaos intermittency regime.     

Oscillator frequency stability improvement by means of negative feedback

A novel, simple method is proposed to increase the frequency stability of an oscillator. An additional negative feedback is used in combination with the positive loop of the harmonic oscillator to decrease the phase sensitivity to fluctuations of parameters other than the resonator. The main advantage of the proposed correction approach is that it does not require expensive external elements such as mixers or resonators. The validity of the method is theoretically demonstrated on a Colpitts oscillator using the control system theory approach and numerical simulations, and is experimentally verified with phase noise measurements of an actual oscillator-mockup. It is shown that the medium-term frequency stability can be easily improved by a factor of ten.     

Controlling gradient phase distributions in a model of active antenna array with locally coupled elements

The regime of synchronization with a certain gradient phase distribution and the possibility of controlling such distribution in a linear array of oscillators coupled by phase-locked loops (PLLs) have been theoretically studied. It is shown that a constant phase progression can be controlled by manipulating collective dynamics, with oscillator eigenfrequencies and coupling coefficients being the control parameters. The proposed principle of control, based on the nonlinear dynamics of PLL-coupled oscillators, can be used in solving the problems of phasing and controlled beam scanning in antenna arrays operating in different frequency bands.     

Model calculations on the influence of dangling bonds on the optical properties of amorphous silicon films

The spectra of the optical constants of amorphous silicon films in the range 0.04hv5.6 eV, especially the very large infrared refractive indices obtained with high deposition rates, are fitted by the classical oscillator model. The oscillators considered are the three strongest single-crystal oscillators and an additional oscillator the existence of which can be ascribed either to dangling bonds in the microcrystal model or to an average non-covalent share of the bonds in the random network model. The sum of the four oscillator strengths is nearly independent of the degree of amorphousness. The calculated oscillator strength of the additional oscillator is proportional to the measured concentration of unpaired spins. The energy states of this oscillator in the E(k) diagram are placed along the axis Γ-L, and are parallel to the edges of the valence and conduction bands at a distance of 0.7±0.1 eV from the valence band.     

The ISSP Tokyo rotating cryostat

The rotating dilution refrigerator has been built up and tested to study topology and dynamics of vortices in thin helium films in porous glasses. The torsional oscillator method is considered as the basic technique to be used. We are able to rotate the cryostat with angular velocity up to 6.3 rad/s and resolve changes of about 0.3 mrad/s. The 40mK minimum temperature of the cryostat does not change up to the highest angular velocities.