Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

THE NONLINEAR INTERACTION OF VORTEX RINGS WITH A FREE SURFACE

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.

NONLINEAR STABILITY ANALYSIS OF A SANDWICH SHALLOW CYLINDRICAL PANEL WITH ORTHOTROPIC SURFACES

In this paper, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthoiropic surfaces. The critical point is determined and the postbitckling behaviour of the panel is studied.

Dual Branches of MHD Three-Dimensional Rotating Flow of Hybrid Nanofluid on Nonlinear Shrinking Sheet

In this study,magnetohydrodynamic(MHD)three-dimensional(3D)flow of alumina(Al2O3)and copper(Cu)nanoparticles of an electrically conducting incompressible fluid in a rotating frame has been investigated.The shrinking surface generates the flow that also has been examined.The single-phase(i.e.,Tiwari and Das)model is implemented for the hybrid nanofluid transport phenomena.Results for alumina and copper nanomaterials in the water base fluid are achieved.Boundary layer approximations are used to reduce governing partial differential(PDEs)system into the system of the ordinary differential equations(ODEs).The three-stage Lobatto IIIa method in bvp4c solver is applied for solutions of the governing model.Graphical results have been shown to examine how velocity and temperature fields are influenced by various applied parameters.It has been found that there are two branches for certain values of the suction/injection parameter b:The rise in copper volumetric concentration improved the velocity of hybrid nanofluid in the upper branch.The heat transfer rate improved for the case of hybrid nanofluid as compared to the viscous fluid and simple nanofluid.

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

NUMERICAL SIMULATIONS OF HIGHLY NONLINEAR STEADY AND UNSTEADY FREE SURFACE FLOWS

A numerical simulation model based on an open source Computational Fluid Dynamics （CFD） package-Open Field Operation and Manipulation （OpenFOAM） has been developed to study highly nonlinear steady and unsteady free surface flows. A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid （VOF） method. The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells. Both steady and unsteady free surface flows are simulated, which include： （1） a submerged NACA0012 2-D hydrofoil moving at a constant speed, （2） the Wigley hull moving at a constant speed, （3） numerical wave tank, （4） green water overtopping a fixed 2-D deck, （5） green water impact on a fixed 3-D body without or with a vertical wall on the deck. The numerical results obtained have been compared with the experimental measurements and other CFD results, and the agreements are satisfactory. The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.

Third-order nonlinear phenomenon generated on the inner surface of bulk lithium niobate crystals with magnesium doping

When two synchronized laser beams illuminate the inner surface of bulk lithium niobate crystals with magnesium doping(5%/mol MgO:LiNbO_(3))under the condition of total reflection,semi-degenerate four-wave mixing(FWM)is generated.On this basis,a more sophisticated frequency conversion process on the interface of nonlinear crystal has been researched.The generation mechanism of FWM is associated with the fundamental waves reflected on the inner surface of the nonlinear crystal.Analysis of the phase-matching mechanism confirms that the FWM is radiated by the third-order nonlinear polarized waves,which are stimulated by the third-order nonlinear susceptibility coefficient of the nonlinear crystal.Theoretically calculated and experimentally measured corresponding data have been presented in this article.These results are expected to provide new inspiration for further experimental and theoretical research on frequency conversion in nonlinear crystals.

Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects

The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.

NUMERICAL SIMULATION OF HIGH TURBULENT FREE SURFACE FLOW UNDER THE CURVILINEAR COORDINATES

This paper presents a new numerical method to simulate the high velocity turbulent flow with free surface by solving two-dimensional incompressible unsteady Navier-Stokes Eqs. , together with the k-ε turbulence model. In order to treat the non-rectangular boundary (or curvilinear boundary), orthogonal boundary-fitted grid is used and the Navier-Stokes Eqs. and k-ε turbulence model are rewritten and discreted in orthogonal curvilinear coordinates. Meanwhile, gas-liquid two-field model theory is introduced to treat the free-surface problem.

Observer-based adaptive sliding mode backstepping output-feedback DSC for spin-stabilized canard-controlled projectiles

This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles.Uniformly ultimate boundedness and tracking are achieved,exploiting a heavily coupled,bounded uncertain and highly nonlinear model of longitudinal and lateral dynamics.In order to estimate unmeasurable states,an observer is proposed for an augmented multiple-input-multiple-output（MIMO） nonlinear system with an adaptive sliding mode term against the disturbances.Under the frame of a backstepping design,an adaptive sliding mode output-feedback dynamic surface control（DSC） approach is derived recursively by virtue of the estimated states.The DSC technique is adopted to overcome the problem of ‘‘explosion of complexity＂ and relieve the stress of the guidance loop.It is proven that all signals of the MIMO closed-loop system,including the observer and controller,are uniformly ultimately bounded,and the tracking errors converge to an arbitrarily small neighborhood of the origin.Simulation results for the observer and controller are provided to illustrate the feasibility and effectiveness of the proposed approach.

What are Exciting in Laser Science

Recent advances in selected areas of laser science are briefly reviewed. They include laser technology, coherent control of quantum systems by lasers, X ray generation by ultrashort high intensity laser pulses, and laser spectroscopic studies of surface catalysis in real environment.