Phase Relation of Harmonics in Nonlinear Focused Ultrasound

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.

Interesting effects in harmonic generation by plane elastic waves

The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic.This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a primary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.

New trajectory linearization control for nonlinear systems undergoing harmonic disturbance

This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.

Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators

In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.

Interaction tonal noise generated by contra-rotating open rotors

Fast and accurate prediction of sound radiation of Contra-Rotating Open Rotors(CRORs)is an essential element of design methods of low-noise open rotor propulsion systems.In the present work,a previous frequency-domain model is extended to predict CROR noise.It builds explicitly the relationship between harmonic loadings and corresponding tonal noise,by which the influential parameters to noise generation can be clearly understood.The real distribu-tions of steady and unsteady blade loadings are calculated by the Nonlinear Harmonic(NLH)method.In the present hybrid approach,both the CFD and acoustic modules are solved in the fre-quency domain.To assess the accuracy of the developed method,the loading noise of a CROR is calculated and compared against results by using the time-domain FW-H module of NUMECA.The predicted sound directivities by the two methods are in good agreements.The present acoustic model in the frequency domain is proven to be accurate and have high efficiency in far-field noise prediction and data processing.Furthermore,the characteristics of the CROR interaction tonal noise are analyzed and discussed.

Relationship between Dislocation Density in P91 Steel and Its Nonlinear Ultrasonic Parameter

P91 steel is an important bearing material used in nuclear power plants. The study of its mechanical degradation behavior is important for ensuring safe operation. The relationship between the dislocation density of P91 steel under different strains and the corresponding nonlinear ultrasonic parameter β was studied. The dislocation density of strained samples was estimated by X-ray diffraction. Nonlinear ultrasonic testing was conducted to evaluate β, showing that this value increased with increasing dislocation density induced by different tensile elongations. It was shown that the ultrasonic secondharmonic generation technique can effectively evaluate the degradation behavior of metallic materials, and the prediction of the residual life of bearing parts in service can be made based on β and the dislocation density.

Strong optical nonlinearities of self-assembled polymorphic microstructures of phenylethynyl functionalized fluorenones

Highly efficient nonlinear optical（NLO） materials with well-defined architectures in the wavelength and subwavelength length scales are of particular importance for next generation of integrated photonic circuits. Fluorenone analogues have been demonstrated to be promising candidates as building blocks for assembly of organic NLO materials thanks to their synergistic supramolecular interactions and brilliant optical properties. Here we have studied the polymorphs of a phenylethynyl functionalized fluorenone derivative, and their controlled self-assembly for microstructures with different morphologies. These polymorphic microcrystals exhibit very distinctive NLO properties, highly related to their supramolecular and electronic structures.

The Fabrication and SHG Test of QPM Periodically Poled KTiOPO_4

The Quasi-phase-matching periodically poled flux-grown KTP by high electrical field method is researched. A 8×5×1mm3,∧=9.0μm PPKTP wafer is successfully fabricated for the first order QPM SHG. The interactive length of the sample is about 3mm. The SHG scheme of Nd: YAG at 1064nm tested that the output power of cw 532nm green light is 0.2mw at room temperature with fundamental power of 1.2w. The normalized conversion efficiency is about 0.09% (W·cm)-1.

Electro-optically tunable self-focusing and self-defocusing in KTP crystals by a cascaded second-order process

We report the transformation of a linear electro-optically tunable non-phase-matched second-order nonlinear process into a cascaded second-order nonlinear process in a bulk KTP crystal to generate the effect of electrooptically tunable Kerr-type nonlinearity. By applying an electric field on the x–y plane, parallel to the z-axis of the crystal, phase mismatch is created, which introduces a nonlinear phase shift between the launched and reconverted fundamental waves from the generated second harmonic wave. Due to the nonuniform radial intensity distribution of a Gaussian beam, a curvature will be introduced into the fundamental wavefront, which focuses or defocuses the incident beam while propagating through the crystal.