Rail and armature current distributions in electromagnetic launchers

The current and magnetic field distributions in the rails and armature of an electromagnetic launcher are obtained in closed form for the steady state. These solutions assume that the armature moves with a steady velocity and account fully for the two-dimensional skin effect caused by the relative motion between the rails and the armature. Both solid and laminated armatures are considered. It is found in the case of the laminated armature that the phenomenon can be described by a single dimensionless parameter,frac{ell}{w}frac{sigma_{o}}{sigma_{r}}sqrt{frac{uell}{pieta_{r}}}.     

On the propagation of waves in an electromagnetic elastic solid

The coupling of electromagnetic and elastic waves is considered from the standpoint of linear elasticity and a linearized electromagnetic theory. The problem of plane waves traveling through a uniform magnetostatic field is considered and couplings of the waves are studied. An investigation of the same problem for a uniform electrostatic field shows that the usual plane waves propagate without any change in their phase velocities but that the mechanical waves are accompanied by small fluctuating electromagnetic fields. The problem of the vibration of a free infinite elastic plate in a large magnetostatic field is examined under the assumption that the resulting electromagnetic fields are quasistationary. Frequency equations are obtained for both symmetric and antisymmetric vibrations and the damping caused by the field for both the first two symmetric and antisymmetric modes is obtained as a linear correction to the usual free plate frequencies.     

Current scaling of projectile velocities with and without asnowplow effect in electromagnetic launchers

Scaling laws are studied, with and without a snowplow (SP) effect, for macroparticle projectile velocities in electromagnetic launchers (EMLs) as a function of the peak EML current. Analytical formulae to predict the instantaneous position and velocity have been derived for both phases of rising and constant EML currents. The SP effect altered the scaling law of the short-pulse muzzle velocity (ν_xw), but not of the long-pulse muzzle velocity (ν_xm). The absolute values of both ν_xw and ν_xm are, however, seriously reduced in the SP regime, depending on the newly introduced parameter, ∈, which is a mass ratio of the armature/projectile system to the gas in the barrel. The critical ∈ s with which the SP effect alters the muzzle velocity and time by more than 10% are presented. Numerical examples are given for possible applications of EMLs on calibrated impact damage testers and impact thermonuclear fusion, where short (1 m) and long (1 km) barrels are to be used for projectiles of several grams to achieve the maximum velocities of 1 and 130 km/s, respectively     

Ohmic heating losses in cryoresistive pulsed energy storage aluminium inductors for electromagnetic launchers

Analytic procedures are developed for calculating the ohmic heating loss for various cryoresistive magnetic energy storage coil configurations that are used to deliver periodic short huge bursts of energy to electromagnetic launchers (railguns). Simple geometries such as long solenoids, continuous winding toroids, low aspect ratio dipoles or straight wire are considered as examples. The effect of cabling on reducing eddy current losses is addressed in detail.     

A finite-element method for the prediction of joule heating ofconductors in electromagnetic launchers

The authors describe a method based on a magnetic vector potential development for calculating the joule heating of the conductors in arbitrary launcher geometries. The method accounts for the effects of varying conductivity of the launcher's materials and can be implemented using available two-dimensional finite-element diffusion codes. Conductor temperature distributions as functions of time for a selected launcher geometry are provided to demonstrate the method     

Coupled electromagnetic and elastic waves in random media

In this paper we have considered the wave propagation in a random medium embedded in a constant primary magnetic field after Karal[l]. The deviation of the magnetic permeability from homogeneity affects the frequency of the wave. A particular case taken the correlation, $\text{R}{}_{\mathrm{\mu 2\mu 2h}}\text{= <μ3}{}^2$$\text{e}{}^{\mathrm{?r/a}}$ where $\text{a}$ is the correlation length of inhomogeneity, has been considered.     

Localization of intense electromagnetic waves in plasmas

We present theoretical and numerical studies of the interaction between relativistically intense laser light and a two-temperature plasma consisting of one relativistically hot and one cold component of electrons. Such plasmas are frequently encountered in intense laser-plasma experiments where collisionless heating via Raman instabilities leads to a high-energetic tail in the electron distribution function. The electromagnetic waves (EMWs) are governed by the Maxwell equations, and the plasma is governed by the relativistic Vlasov and hydrodynamic equations. Owing to the interaction between the laser light and the plasma, we can have trapping of electrons in the intense wakefield of the laser pulse and the formation of relativistic electron holes (REHs) in which laser light is trapped. Such electron holes are characterized by a non-Maxwellian distribution of electrons where we have trapped and free electron populations. We present a model for the interaction between laser light and REHs, and computer simulations that show the stability and dynamics of the coupled electron hole and EMW envelopes.     

Elastic waves in multiferroic cylinders of sectorial cross-section

The propagation of elastic waves in multiferroic cylindrical waveguides of sectorial cross-section is analyzed based on the linear theory of electro-magneto-elasticity. A wave potential method is adopted to derive analytically the characteristic equations, from which the dispersion relations are readily obtained. Representative examples are performed to investigate the essential characteristics of the waves by looking into the real, imaginary and complex branches of full dispersion spectra. It is found that phase velocities and cutoff frequencies depend considerably on the waveguide’s angular measure, which should be a significant factor to control the dispersion characteristics of the multiferroic waveguide of specific materials. Furthermore, a two-layer model is also presented to compare with the single model.     

Elastic stresses between curved bodies in rolling contact

An outline of the development of the elastic theory of contact stresses is presented. The literature is discussed in some detail, and equations for the sub-surface stresses are given for several important cases. The effects of surface shear stresses associated with tangential forces and rolling with spin are also considered.     

Elastic waves in multiferroic cylinders of sectorial cross-section

The propagation of elastic waves in multiferroic cylindrical waveguides of sectorial cross-section is analyzed based on the linear theory of electro-magneto-elasticity. A wave potential method is adopted to derive analytically the characteristic equations, from which the dispersion relations are readily obtained. Representative examples are performed to investigate the essential characteristics of the waves by looking into the real, imaginary and complex branches of full dispersion spectra. It is found that phase velocities and cutoff frequencies depend considerably on the waveguide’s angular measure, which should be a significant factor to control the dispersion characteristics of the multiferroic waveguide of specific materials. Furthermore, a two-layer model is also presented to compare with the single model.     

Stress analysis of the rails of a new high velocity armature design in an electromagnetic launcher

In an electromagnetic launcher, the magnetic field creates a dynamic force that moves the armature forward. In an electromagnetic launcher, the armature reaches a critical velocity during the launch which causes high amplitude stress and strain. In addition, high stress and strain damage the rails and reduces its life span. The purpose of this paper is to investigate the effect of armature velocity as well as the rails physical and geometrical properties on the dynamic response of the rails in an electromagnetic launcher. In this study the second moment of inertia of the rails cross-section, Young modulus, foundation stiffness and density of the rails are constant in location and time. In our formulation of governing non-linear differential equations, Maxwell equations and deflection equation are applied to the rails under dynamic loading. To solve the non-linear governing differential equations a finite difference method is utilized.     

Elastic moduli of Al-Si and Al-Ge solid solutions

The elastic moduli of Al-Si and Al-Ge alloys obtained by solid-solution under pressure are investigated theoretically using a previous treatment based on the microscopic electronic theory. The obtained results for elastic coefficients such as bulk modulus, shear modulus, Young's modulus and Poisson's ratio for matrix Al are in good agreement with temperature-dependent experimental data. These moduli of Al-Si and Al-Ge alloys are calculated, and the concentration dependence of the elastic data is presented quantitatively.     

Elastic waves in multilayered plate reinforced by inextensible fibres

In this article the propagator matrix method is employed to obtain the overall transfer matrix which gives dependence of displacements and stresses on the one face of the multilayered plate in terms of those on the opposite face. Attention is restricted to waves propagating in the plane parallel to stress free plate faces where we examine waves travelling at any angle to one of the families of fibres. The plate is of finite thickness but of infinite lateral extent. Each of the laminae is formed from same material reinforced by one family of inextensible fibres laying in the plane of the laminae. Results are presented for eight-ply laminated plate with symmetric arrangements of the laminae. Frequency spectrum for first 10 modes is presented for specific plate with (/2, –/4, /4, 0)_s lay up, and specific fibre reinforced material.     

Elastic waves in a fluid-loaded, semi-infinite axisymmetric rod

In a fluid-loaded, semi-infinite axisymmetric rod, a free shear stress boundary condition on the circular cross-sectional end introduces complicated, nondispersive waves in the solid. They are composed of a pulse wave, which has the same waveform as the transmitted one and travels at speed c1, and different kinds of pulse trains, each of which travels along the rod at the speed of either c1 or square root of 2c2, where c1 and c2 are the propagating speeds of the longitudinal and transversal bulk waves, respectively. Furthermore, one can conclude from the solutions to the boundary conditions that c1 and square root of 2c2 are the only phase speeds of nondispersive waves. Frequency equations associated with these waves are established, and the solutions are solved and discussed analytically and numerically. The acoustic field in the fluid is also fully discussed, and it is more complicated than a single outgoing Hankel function as described for an infinite rod. The acoustic energy coupling between the solid and the fluid and the end reflection and transmission are quantified as well. In the end, experimental examinations of the echo spectra, using an aluminum rod immersed in the water and air, fully confirm the numerical solutions to the frequency equations.     

高频电磁力作用下金属液内电磁超声波的生成

为解决由机械振动产生的超声波无法在高温环境中成功应用的难题，提出了利用静磁场和交流电流、静磁场和交流磁场的相互作用分别在金属液内直接生成高强度电磁超声波的方法，运用超声波压力传感器对用这两种方法在金属液内生成的电磁超声波的强度进行了测量。研究表明：电磁超声波的强度与所施加的高频电磁力的强度成正比，频率与电磁力的频率相同；实验结果和理论解析结果基本一致；利用高频电磁力的局部作用在金属液全场范围内生成的电磁超声波可以在金属精炼及凝固过程中获得广泛应用。     

Elastic waves in randomly stratified medium. Numerical calculations

Summary The propagation of elastic harmonic waves through a stratified slab is investigated. It is assumed a nonzero angle of inclination of an incident wave. The equations for the amplitudes of reflected and transmitted waves obtained in reference [1] are transformed to a form more convenient for numerical calculations and generalized for more complicated laminates. an example of the elastic waves propagating through the steel-titanium laminate in aluminimm environment is studied numerically. The limiting case where the density of stratification of the slab tends to infinity is analyzed. The dependence of the effective reflection properties on the material parameters of the strata is presented.     

Elastic waves in randomly stratified medium. Analytical results

Summary Propagation of elastic harmonic waves through a stratified slab is investigated. It is assumed a nonzero angle of inclination of an incident wave. The equation for the amplitudes of reflected and transmitted waves are presented in the form useful for simulation. Then a limiting case where the density of stratification of the slab tends to infinity is analysed and the equations for the amplitudes of the waves in a homogenized medium are obtained. Finally, the law of large numbers for noncommuting random products is applied to the randomized equation for amplitudes showing its convergence to some deterministic effective one for increasing density of stratification.     

Thermoelastic plane waves in a rotating solid

Summary Plane waves in a homogeneous and isotropic unbounded thermoelastic solid rotating with a uniform angular velocity are discussed in the context of the generalised thermoelasticity theory of Green and Lindsay. The effects of rotation of the body on the phase velocity, energy loss and decay coefficient are discussed in some detail for waves of small and large frequencies, and for small coupling between the thermal and mechanical fields. Results of earlier works are deduced as particular cases of the more general results obtained here.     

Thermal shock waves in nonlinear solid media

Heat transfer of the wave character is considered in linear and nonlinear media on the basis of a new law of the heat conduction with allowance not only for the first and second order temporal derivatives of the heat flux, but the higher order derivatives as well. This allowed us to reduce the heat transfer that was studied on the basis of a hyperbolic equation to a task about the heat transfer described by a parabolic equation with a retarded time argument. It is shown that under certain conditions for the heat transfer at free boundaries, the discontinuities of the first kind arising in the temperature distribution in nonlinear media are trans-formed to compression wave heat fluxes. The results obtained here confirm the assumptions made. The results can be used in designing the heat transfer in hypersonic vehicles under conditions of high-intensity aero-gas-dynamic and radiation heating.