A Study on Super Speed Forming of Metal Sheet by Laser Shock Waves

Metal sheet plastic deformation or forming is gener at ed through a mechanical pressure or a thermal variation. These pressure variatio ns or thermal variations can be created by a variety of means such as press form ing, hydroforming, imploding detonation and so on. According to the magnitude of the strain rates all these forming methods can be divided into quasi-static fo rming and dynamical forming. Up to now there are no reports of forming methods w ith the strain rates above 10 5sec -1, even though the exploding forming. In this article, we work on a dynamic super-speed forming method driven by lase r shock waves and advanced a novel concept of laser shock forming. The initial o bservation of the laser shock forming is done through a bugle testing with speci mens of SUS430 sheet metal, using a neodymium-glass laser of pulse energy 10J～ 3 0J and duration of 20 ns (FWHM). The investigation revealed that the plastic de formation during the laser shock forming is characterized as ultrahigh strain ra te up to 10 7sec -1. We indicate that plastic deformation increases nonlin early when the energy density of the laser varies. By investigating the hardness and residual stress of the surfaces, we conclude that laser shock forming is a combination technique of laser shock strengthening and metal forming for introdu cing a strain harden and a compressive residual stress on the surface of the wor k-piece, and the treated surface by laser shock forming has good properties in fatigue and corrosion resistance. This technique can achieve forming wit h or without mould.

Improved form of wind wave frequency spectrum

The lower frequency part of the theoretical wind wave spectrum proposed by the authors (Wen et al. , 1988a, b,c) has been improved and the form of spectrum is appreciably simplified. In addition to the field data collected in the Bohai Sea region and used in the previous papers, those obtained in the Huanghai Sea, the East China Sea and the South China Sea have been employed so that the improved spectra can be verified on a more extensive observational basis. Computed results agree with the observations well. Further comparisons have been made between the proposed spectra and the JONSWAP spectrum. Though the two types of spectrum are close to each other in form, the former shows, as a whole, better agreement with the observation than the latter. By introducing an improved relation between the peak-ness factor and significant wave steepness, the spectrum contains only significant wave height and period as parameters. For spectra given in this form, the computed peak frequencies coincide approximately with observed values and the computed peak magnitudes of spectra agree basically with observations, but, because of the statistic variability inherent in the measurements of significant wave heights and periods, there are certain discrepancies between computed and measured spectrum peak magnitudes.

Parameters in wind-wave frequency spectra and their bearings on spectrum forms and growth

The spectrum variance m0, peak frequency ω0 and peakness factor p are expressed in terms of nondimensional fetch and duration by making use of relations which are derived through comparing and analyzing existing empirical formulas for the growth of significant wave height and period. The main features of spectrum growth as specified by these parameters agree with those of the JONS-WAP experiments. For given wind speed and fetch, the high frequency parts beyond the peaks of shallow water spectra almost coincide with that of the corresponding deep water spectrum, whereas the low frequency parts differ appreciably. The method developed in this paper predicts smaller significant wave height as well as smaller wave period for shallow water spectra in contrast to the theoretical result of Kitaigorodskii ef al, in which the peak frequency, and consequently the significant wave period, remains basically unchanged for different water depths. Spectra are further reduced to a form in which only significant wave height and period are left as parameters, the peakness factor being replaced by the wave steepness through an empirical relation between them. Spectra in this form have been verified by observations.

A Study on the Spectral Form of Nearshore Water Waves

The spectral form of wind waves is investigated based on the ocean wave data observed at three nearshore stations of Taiwan. In this study, the generalized forms of Pierson-Moskowitz spectrum and JONSWAP spectrum are used to describe the local wave spectrum by selecting suitable spectral form parameters. It is shown that, at a specific site, the similarity of wave spectral form exists. Thus it is possible to use a representative spectral form for a given nearshore region to describe the wave spectrum at this nearshore. On the other hand, the effects of relative water depth on spectral form are examined. The feasibility of two spectral models in finite water depth is evaluated by using the same field wave data.

A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation

In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.

Numerical Prediction of Form Factor and Wave Interference of A Trimaran for Different Outrigger Positions

Trimaran hydrodynamics have been an important research topic in recent years.Trimarans have even been chosen for naval surface combatants.In this case,investigation of a trimaran with different outrigger positions is important and necessary for better hydrodynamic performance.This paper focuses on the numerical investigation of trimaran hydrodynamics.The trimaran model used in this study is a 1/80 scale high-speed displacement frigate-type concept developed by the Center for Innovation in Ship Design(CISD)at Naval Surface Warfare Center,Carderock Division(NSWCCD).The numerical simulations were conducted for different outrigger positions at low and moderate Froude numbers by using commercial CFD software solving URANS equations.A verification and validation study was carried out for the numerical method in one configuration and one ship velocity.The existing experimental results for the trimaran resistance in the literature were used for validation.Five different outrigger positions were analyzed and the form factor of each configuration was calculated by the Prohaska method.The total resistance was decomposed to its components using the form factor.The interference factor was calculated for each configuration in terms of total resistance,residual resistance and wave resistance.Also,wave profiles using the longitudinal wave cuts in different locations were obtained both numerically and experimentally.It was concluded that the outrigger position had different effects on the interference,total resistance and wave profile at different Froude numbers.It was also shown that the CFD results were in good agreement with the experimental data in all configurations.In conclusion,this study presents the results of interference effects for different trimaran configurations in terms of wave resistance in addition to the total resistance and residual resistance.The numerical method was validated not only with the total resistance test data but also the longitudinal wave profiles along the hull.

Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to （1＋1）-Dimensional Dispersive Long Wave Equation

In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

New Rational Form Solutions to Coupled Nonlinear Wave Equations

The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.

Photons in the Non－uniform Optical Waveguide Propagate along z－axis in Spiral Form

This paper gives the strict solution of optical field equation in the optical waveguides with parabolic profiles. It shows that the photons in the non-uniform optical waveguide propagate along z-axis in spiral form, just like a charged particles moving in the magnetic field. Only in the step-index waveguides, it can the photons propagate in ziging form.

New Families of Rational Form Solitary Wave Solutions to （2＋1）-Dimensional Broer-Kaup-Kupershmidt System＊

Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.

Key technologies of roll forming automobile components with AHSS

Lightweight design is one of the development trends of the automobile industry. An effective way to achieve lightweight auto bodies is to use AHSS （advanced high strength steel ） for the safety components of automobiles. This study has taken doorsill reinforcements made of martensite AHSS as the object ,and performed research on the AHSS roll forming technologies and prototype development of typical asymmetric open components. By means of finite element analysis （FEA） and simulation,studies have been carried out on the springback and edge wave defects during AHSS roll forming ,and an optimized process design has been achieved. The generation mechanisms of vertical bows ,horizontal cambers, twists,pre-punched hole distortion and cut end flare have been analyzed,and solutions to these defects have been given. In addition,tesing of the roll forming process for AHSS has been conducted and typical samples with required dimensional accuracy have been manufactured. This study has provided technical support for the large-scale application of AHSS.

New rational form solutions to mKdV equation

In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.

New Exact Periodic Solitary-Wave Solutions for New (2+1)-Dimensional KdV Equation

The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.

Lump,lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.

基于Qform的波浪轴楔横轧成形有限元仿真

分析了某型波浪轴楔横轧成形原理及工艺,运用有限元软件Qform建立了其仿真模型,对其在楔横轧成形过程中的温度、等效应力、等效应变、变形量等进行了仿真分析。结果表明:波浪轴在楔横轧成形过程中的等效应力、等效应变最大值主要分布在横轧部位及其中间压轧部位,且其变化趋势基本一致;毛坯变形量沿着毛坯轴中心向两端先增加后减小。

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.

Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel

A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semi- cylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method.The solution is reduced to solving a set of infinite linear algebraic equations.Fourier expansion theorem with the form of complex exponential function and cosine function is used.Numerical solutions are obtained by truncation of the infinite equations.The accuracy of the presented numerical results is carefully verified.

Study of detonation wave contours in EFP warhead

An analytical model for calculating the propagation time of shock wave in a wave shaper is presented in this study. The calculated results show that the contours of three typical detonation waves, such as conical detonation wave, spherical detonation wave, and planar detonation wave, can be formed in the main charge by changing the thickness of wave shaper.The results show that the planar detonation wave do better than the conical detonation and the spherical detonation wave in increasing the length–diameter ratio of explosively-formed projectiles(EFP) and keep the nose of EFP integrated. The detonation wave can increase the length–diameter ratio of EFP when the wave shaper has the suitable thickness.

Damage of a large-scale reinforced concrete wall caused by an explosively formed projectile(EFP)

To quickly break through a reinforced concrete wall and meet the damage range requirements of rescuers entering the building,the combined damage characteristics of the reinforced concrete wall caused by EFP penetration and explosion shock wave were studied.Based on LS-DYNA finite element software and RHT model with modified parameters,a 3D large-scale numerical model was established for simulation analysis,and the rationality of the material model parameters and numerical simulation algorithm were verified.On this basis,the combined damage effect of EFP penetration and explosion shock wave on reinforced concrete wall was studied,the effect of steel bars on the penetration of EFP was highlighted,and the effect of impact positions on the damage of the reinforced concrete wall was also examined.The results reveal that the designed shaped charge can form a crater with a large diameter and high depth on the reinforced concrete wall.The average crater diameter is greater than 67 cm(5.58 times of charge diameter),and crater depth is greater than 22 cm(1.83 times of charge diameter).The failure of the reinforced concrete wall is mainly caused by EFP penetration.When only EFP penetration is considered,the average diameter and depth of the crater are 54.0 cm(4.50 times of charge diameter)and 23.7 cm(1.98 times of charge diameter),respectively.The effect of explosion shock wave on crater depth is not significant,resulting in a slight increase in crater depth.The average crater depth is 24.5 cm(2.04 times of charge diameter)when the explosion shock wave is considered.The effect of explosion shock wave on the crater diameter is obvious,which can aggravate the damage range of the crater,and the effect gradually decreases with the increase of standoff distance.Compared with the results for a plain concrete wall,the crater diameter and crater depth of the reinforced concrete wall are reduced by 5.94%and 9.96%,respectively.Compared to the case in which the steel bar is not hit,when the EFP hit one steel bar and the intersection of two steel bars,the crater diameter decreases by 1.36%and 5.45%respectively,the crater depth decreases by 4.92%and 14.02%respectively.The EFP will be split by steel bar during the penetration process,resulting in an irregular trajectory.