On disturbances in a semi-infinite visco-elastic rod in a magnetic field

Summary The paper makes use of electromagnetic equations of Maxwell, the equations of mechanical motion together with stress and strain relation of a particular visco-elastic material, to determine the disturbances in it when excited by a magnetic field.     

Propagation of Rayleigh waves on visco-elastic cylindrical surfaces placed in a magnetic field

Summary This paper studies axial Rayleigh waves in visco-elastic cylinder surrounded by vacuum and for body of same material with a cylindrical cavity. Magneto-elastic equations of motion for wave propagation in the radial and axial direction have been solved to obtain frequency equations.     

Rayleigh-waves on cylindrical surfaces of visco-elastic material of general linear type in presence of a magnetic field

Summary The propagation of disturbances in cylindrical surfaces of visco-elastic material of general linear type (i) cylinder surrounded by a vacuum (ii) and on an infinite body of same material having a cylindrical cavity, when the surface is subjected to an initially static magnetic field, making use of the electro-magnetic equations of Maxwell, equations of elasticity and the stress-strain relations of the material.     

Evolution of localized folding for a thin elastic layer in a softening visco-elastic medium

Long compressed elastic struts on softening elastic foundations have a tendency to buckle locally. The same tendency is demonstrated here for the instantaneous response of elastic struts supported by visco-elastic media. A governing nonlinear partial differential equation is derived to describe the evolution of the localized form in time. Under the assumed constant end-shortening this is found to be approximated by a coupled set of seven ordinary differential (diffusion) equations. As the load drops to zero, the localized buckle pattern evolves towards the form of the single long wave, but remains aperiodic for all time. Three-dimensional plots show how this localized pattern changes over time.     

On the propagation of plane waves in a porous visco-elastic material containing a fluid and deformed by a magnetic field

Summary In the present note, an attempt has been made to investigate the wave-motions in a poro-viscoelastic medium traversed by a static magnetic field, by using the equations ofMaxwell, and those ofBiot.     

On disturbances in a visco-elastic medium of Maxwell type in contact with a liquid medium and subjected to a magnetic field

Summary The problem of disturbances in a visco-elastic medium due to Maxwell in contact with a liquid medium — both being perfectly conductive — has been investigated when an impulsive force acts along the plane of the contact. The electro-magnetic equations of Maxwell, equation of elasticity and the stress-strain relations of the material have been used in the investigation.     

On magneto-elastic disturbaces in a visco-elastic cylinder placed in a magnetic field

Summary The present note is an attempt to discuss the disturbances in a cylinder characterised by a visco-elasticity of general linear type, which is subjected to a magnetic field.     

Propagation ofSH-waves in a heterogeneous visco-elastic layer overlying a homogeneous voigt medium

Summary The propagation ofSH-waves in a vosco-elastic layer having variable material properties has been studied to explain the damping phenomenon of the wave motion. The damping coefficient may be calculated and the effect of heterogeneity on such type of wave motion may be observed from the obtained frequency equation.     

Propagation of waves in a visco-elastic half-space due to internal sources

Summary The nature of waves and disturbances generated by a time-periodic concentrated force acting inside a visco-elastic half-space has been studied. Interpretations have been given to the various terms in the expressions for the displacement components.     

Disturbances produced in a visco-elastic medium by transient torsional body forces

Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above.     

On longitudinal vibration of an elastic bar in a magnetic field

Summary The equations of elasticity, electromagnetic equations of Maxwell have been applied to investigate the longitudinal vibration of a partly homogenous, partly inhomogeneous elastic bar permeated by a magnetic field.     

Shear waves at a corrugated interface between anisotropic elastic and visco-elastic solid half-spaces

Rayleigh’s method of approximation is employed to find out the reflection and transmission coefficients due to an incident plane SH wave at a corrugated interface between a laterally and vertically inhomogeneous anisotropic elastic solid half-space and a laterally and vertically inhomogeneous isotropic visco-elastic solid half-space. The lateral and vertical inhomogeneities are described by the exponential variations of elastic parameters. The formulae of reflection and transmission coefficients are derived in closed form for the first-order approximation of the corrugation. The effects of the corrugation of the interface, the inhomogeneity, the anisotropy, the visco-elasticity and the frequency of the incident wave on these coefficients are studied analytically and numerically for a specific model containing a periodic interface. The results of earlier workers have been reduced as particular cases from the present formulation.     

Seismic wave propagating in Kelvin-Voigt homogeneous visco-elastic media

The earth media friction attenuates the energy of seismic wave. Obviously, that earth medium is treated as viscoelasticity is more appropriate than as elasticity. Seismic wave in visco-elastic media contains abundant lithology information of the medium. The investiga-tions of the solutions of visco-elastic wave equations, velocities of seismic wave propagating and the at-tenuation of seismic wave in the visco-elastic media are very important for geophysical prospecting tech-nology. Under a sma…     

Kelvin粘弹性VTI介质中地震波的传播

In this article, under the assumption of weak anisotropy and weak attenuation, we present approximate solutions of anisotropic complex velocities and quality-factors for Kelvin visco-elastic transverse isotropy (KEL-VTI) media, based on the complex physical parameter matrix. Also, combined with the KEL-VTI media model, the propagation characteristics of the qP-, qSV-, and qSH-wave phases and energies are discussed. Further, we build a typical KEL-VTI media model of the Huainan coal mine to model the wave propagation. The numerical simulation results show that the PP- and PSV-wave theoretical wave-fields are close to the wave-fields of three-component P- and converted-waves acquired in the work area. This result proves that the KEL-VTI media model gives a good approximation to this typical coalfield seismic-geologic conditions and is helpful to the study of attenuation compensation of multi-component seismic data.     

A note on disturbances in a certain type of visco-elastic solid deformed by a magnetic field

Summary The present note is an attempt to study the propagation of disturbances in a semiinfinite visco-elastic rod which is of three-parameter type, and which is subjected to a static magnetic field.     

Elastic waves in visco-elastic half-space generated by various vehicle loads

In this paper, the response of a visco-elastic half-space subjected to moving loads with static and dynamic components is investigated. Four types of vehicle loads are considered, including the moving point load, uniformly distributed wheel load, elastically distributed wheel load, and a train load simulated as a sequence of elastically distributed wheel loads. In each case, the influence of the moving loads traveling in the subsonic, transonic and supersonic ranges on the dynamic responses of the half-space is studied. The parametric study conducted herein enables us to grasp insight into the mechanism of wave propagation for a visco-elastic half-space under moving loads.     

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 semicylindrical 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.     

Response of an infinite cylinder with a ridge on the surface to periodic excitation

Summary An infinite cylinder with a small ridge on the surface parallel to the axis is assumed to be excited by an embedded periodic line source radiating compressional waves. The line source is also assumed to lie parallel to the axis, and the frequency of radiation is small enough so that the corresponding wavelength is large compared to the dimension of the ridge on the surface of the cylinder. Considering the effect of the ridge as a small perturbation, the wave equations are solved and the amplitudes of the potential fields are expressed in terms of a set of inhomogeneous algebraic equations in which the solution of the problem without the ridge supplies the source term for the first order perturbation in potential fields.     

三维层状黏弹性半空间中球面SH、P和SV波源自由场

采用刚度矩阵方法结合Hankel积分变换,求解了层状黏弹性半空间中球面SH、P和SV波的自由波场.首先,在柱坐标系下建立层状黏弹性半空间的反轴对称(柱面SH波)和轴对称(柱面P-SV波)情况精确动力刚度矩阵.进而由Hankel变换将空间域内的球面波展开为波数域内柱面波的叠加,然后将球面波源所在层的上下端面固定,求得固定层内的动力响应和固定端面反力,将固端反力反向施加到层状黏弹性半空间上,采用直接刚度法求得固端反力的动力响应,叠加固定层内和固端反力动力响应,求得波数域内球面波源动力响应.最后由Hankel积分逆变换求得频率-空间域内球面波源自由场,时域结果由傅里叶逆变换求得.文中验证了方法的正确性,并以均匀半空间和基岩上单一土层中球面SH、P和SV波为例分别在频域和时域内进行了数值计算分析.研究表明基岩上单一土层中球面波自由场与均匀半空间情况有着本质差异;基岩上单一土层中球面波位移频谱峰值频率与场地固有频率相对应,基岩面的存在使得基岩上单一土层地表点的位移时程非常复杂,振动持续时间明显增长;阻尼的增大显著降低了动力响应的峰值,同时也显著减少了波在土层的往复次数.     

Exact dynamic member stiffnesses for a beam on an elastic foundation

This paper gives exact Bernoulli–Euler dynamic flexural member equations for a uniform beam on an elastic foundation. These enable exact results to be obtained when the beam is included in free or sinusoidally forced vibration calculations for a plane or space frame, at any frequency. In addition, information is presented to ensure that no natural frequencies are missed in a free vibration analysis.