移动荷载下上覆弹性板饱和地基的动力响应

用半解析法对移动条形荷载作用下上覆弹性板饱和两相弹性介质的动力响应问题进行了研究。由忽略土粒压缩和土体自重的Biot波动方程出发,对荷载进行Fourier展开。假设响应函数形式,利用待定系数法求解了考虑固液耦合作用的两相介质在移动荷载作用下的土体位移,有效应力及孔压表达式。求解过程中考虑了土体和弹性板之间的相互作用,并假设土体与弹性板的竖向位移相等。通过计算给出了各参数对土体位移和孔压响应和的影响。数值结果表明弹性梁刚度对位移和孔压响应有较大影响。     

Earth surface response to a load moving in a tunnel

Using the solution of the problem on an elastic half-space subjected to a load uniformly propagating on the surface of a circular cylindrical cavity along its generator parallel to the free boundary of the half-space, we study the stress-strain state of the Earth surface over the tunnel under the action of normal axisymmetric periodic and aperiodic loads moving in the tunnel. Numerical results are analyzed on the basis of the tables and graphs presented in the paper.     

Steady state responses of poroelastic half-space soil medium to a moving rectangular load

The dynamic steady state responses of a poroelastic half-space soil medium subjected to a moving rectangular load are investigated analytically/numerically. The full dynamic poroelastic theory of Biot is employed, under the assumption of an incompressible solid grain and neglecting the apparent mass density. Using the Fourier transform, the governing equations of motion are then reduced to a system of four coupled ordinary differential equations which are solved semi-analytically. Soil vertical displacements, accelerations and pore water pressures induced by moving load are calculated. Computed result shows that load velocity and intrinsic permeability of the soil medium shows an apparent effect on its dynamic responses and pore water pressures.     

Dynamic displacements of an infinite beam on a poroelastic half space due to a moving oscillating load

This investigation is concerned with the dynamic displacements of a beam on a poroelastic half space under a periodic oscillating load of constant velocity. The governing equations for the proposed analysis are solved using Fourier transform. The expression for the vertical displacement is obtained according to the contact condition between a beam and a half space. The effects of the moving velocity and vibration frequency of the load on the dynamic displacement are considered in the numerical examples. The results show that the load velocity has significant influence on dynamic displacement. It is also noted that large differences exist between the dynamic responses for a beam on a poroelastic half space and on an elastic half space when the load velocity is larger than the shear wave speed of the medium. The reported work is supported by the National Natural Science Foundation of China (Project No. 10372073).     

Response of railway track system on poroelastic half-space soil medium subjected to a moving train load

Based on the dynamic poroelastic theory of Biot, dynamic responses of a track system and poroelastic half-space soil medium subjected to moving train passages are investigated by the substructure method. The whole system is divided into two separately formulated substructures, the track and the ground, and the rail is described by introducing the Green function for an infinitely long Euler beam subjected to the action of moving axle loads of the train and the reactions of the sleeper. Sleepers are represented by a continuous mass and the effect of the ballast is considered by introducing the Cosserat model for granular medium. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency-wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain train speed. Computed results show that the shape of the rail displacements of the elastic and poroelastic soil medium are in good agreement with each other of the low train velocity, but the result of the poroelastic soil medium is significantly different to that of the elastic soil medium for the high train velocity which is higher than Rayleigh-wave speed in the soil. The influence of the soil intrinsic permeability on soil responses is discussed with great care in both time domain and frequency domain. The dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.     

Out-of-plane responses of a circular curved Timoshenko beam due to a moving load

For the cases of using the finite curved beam elements and taking the effects of both the shear deformation and rotary inertias into consideration, the literature regarding either free or forced vibration analysis of the curved beams is rare. Thus, this paper tries to determine the dynamic responses of a circular curved Timoshenko beam due to a moving load using the curved beam elements. By taking account of the effect of shear deformation and that of rotary inertias due to bending and torsional vibrations, the stiffness matrix and the mass matrix of the curved beam element were obtained from the force–displacement relations and the kinetic energy equations, respectively. Since all the element property matrices for the curved beam element are derived based on the local polar coordinate system (rather than the local Cartesian one), their coefficients are invariant for any curved beam element with constant radius of curvature and subtended angle and one does not need to transform the property matrices of each curved beam element from the local coordinate system to the global one to achieve the overall property matrices for the entire curved beam structure before they are assembled. The availability of the presented approach has been verified by both the existing analytical solutions for the entire continuum curved beam and the numerical solutions for the entire discretized curved beam composed of the conventional straight beam elements based on either the consistent-mass model or the lumped-mass model. In addition to the typical circular curved beams, a hybrid curved beam composed of one curved-beam segment and two identical straight-beam segments subjected to a moving load was also studied. Influence on the dynamic responses of the curved beams of the slenderness ratio, moving-load speed, shear deformation and rotary inertias was investigated.     

Dynamic effects of moving load on a poroelastic soil medium by an approximate method

The problem of the dynamic response of a fully saturated poroelastic soil stratum on bedrock subjected to a moving load is studied by using the theory of Mei and Foda under conditions of plane strain. The applied load is considered to be the sum of a large number of harmonics with varying frequency in the form of a Fourier expansion. The method of solution considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer near the free surface of the medium. Both problems are solved analytically in the frequency domain. The effects of the shear modulus, permeability and porosity of the soil medium and the velocity of the moving load on the dynamic response of the soil layer are numerically evaluated and compared with those obtained by the exact solution of the problem. It is concluded that for fine poroelastic materials, the accuracy of the present method against the exact one is excellent.     

Effects of irregularity and initial stresses on the dynamic response of viscoelastic half-space due to a moving load

The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space due to a load moving with a constant velocity at a rough free surface.Expressions for normal and shear stresses are obtained in closed form. The substantial effects of influence parameters, viz., depth(from the free surface), irregularity factor, maximum depth of irregularity, viscoelastic parameter, horizontal and vertical initial stresses,and frictional coefficient, on normal and shear stresses are investigated. Moreover, comparative study is carried out for three different cases of irregularity, viz., rectangular irregularity,parabolic irregularity and no irregularity, which is manifested through graphs.     

P波作用下饱和土中深埋圆形复合式衬砌隧道动应力响应研究

采用波函数展开法,推导出了平面P波入射下饱和土中深埋圆形双层衬砌动应力集中问题的解析解,并将该解退化为弹性介质中双层衬砌对平面P波散射的稳态解,验证了计算结果的正确性。研究结果表明,饱和土中双层衬砌的内边界动应力集中系数值大于外边界;外侧衬砌及内侧衬砌弹性模量对衬砌的动应力集中系数影响较大,在保证外侧衬砌稳定性较好的条件下,内侧衬砌尽可能选择刚度较小的材料;增加外侧衬砌及内侧衬砌的厚度可明显地减小衬砌内的动应力集中系数。     

Ground vibration due to a high-speed moving harmonic rectangular load on a poroviscoelastic half-space

The transmission of vibrations in the ground, due to a high-speed moving vertical harmonic rectangular load, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as a totally or partially saturated porous viscoelastic half-space, using the complete Biot theory. The solutions in the transformed domain are obtained using a double Fourier transform on the surface spatial variables. A modified hysteretic damping model defined in the wavenumber domain is used, first presented by Lefeuve-Mesgouez et al. [Lefeuve-Mesgouez, G., Le Houédec, D., Peplow, A.T., 2000. Vibration in the vicinity of a high-speed moving harmonic strip load. Journal of Sound and Vibration 231(5) 1289–1309]. Numerical results for the displacements of the solid and fluid phases, over the surface of the ground and in depth, are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the medium.     

Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space

The present study aims to study the normal and shear stresses produced in a rough irregular heterogeneous monoclinic half-space due to a normal moving load. Closed form expressions of normal and shear stresses have been obtained. It is observed that both normal stress and shear stress are affected not only by depth, the frictional coefficient on a rough surface, and the maximum depth of irregularity but also by the heterogeneity and types of irregularity in the medium. The comparative study has been made to analyze the effect of different types of irregularity on both the stresses. There is a significant effect of depth, frictional coefficient, heterogeneity, maximum depth of irregularity and irregularity factor on the normal and shear stresses in both heterogeneous monoclinic and heterogeneous isotropic medium. A comparison is made to study the effects of the said parameters on the normal and shear stress produced in both heterogeneous medium. These effects are highlighted and depicted by means of graphs. As a special case of the problem, the stress produced due to normal moving load in an isotropic half-space with and without heterogeneity, irregularity has been discussed.     

Wavelet approach to vibratory analysis of surface due to a load moving in the layer

The paper analyses theoretically the surface vibration induced by a point load moving uniformly along a infinitely long beam embedded in a two-dimensional viscoelastic layer. The beam is placed parallel to the traction-free surface and the layer under the beam is assumed to be a half space. The response due to a harmonically varying load is investigated for different load frequencies. The influence of the layer damping and moving load speed on the level of vibrations at the surface is analysed and analytical closed form solutions in the integral form for the displacement amplitude and the amplitude spectra are derived. Approximate displacement values depending on Young’s modulus and mass density of layers are obtained. The mathematical model is described by the Euler–Bernoulli beam equation, Navier’s elastodynamic equation of motion for the elastic medium and appropriate boundary and continuity conditions. A special approximation method based on the wavelet theory is used for calculation of the displacements at the surface.     

Vibration of beams with general boundary conditions due to a moving random load

Summary  The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed, and fixed–free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation. Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force on the dynamic response of beams are studied in detail. Received 3 December 2001; accepted for publication 30 April 2002     

Effect of imperfect bonding on the dynamic response of a pre-stressed sandwich plate-strip with elastic layers and a piezoelectric core

In this paper,we consider the dynamic response of a pre-stressed sandwich plate-strip with a piezoelectric core and elastic layers under the action of a time-harmonic force resting on a rigid foundation.The investigation is carried out within the framework of the piecewise homogeneous body model by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity.It is assumed that there is a shear-spring-type imperfect contact between the layers,but a complete contact between the plate-strip and the rigid foundation.A mathematical model of the problem is constructed,and the governing equations of motion are solved by employing the finite element method(FEM).Numerical results illustrating the influence of a change in the value of the shear-spring parameter on the dynamic response of the plate-strip are then presented.     

Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation

The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the efects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial differential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge–Kutta method. Moreover, the efects of diferent truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.     

On the response of an elastic membrane to a travelling ring load

Exact solutions in closed-form are presented for the dynamic response of an infinite elastic membrane to a suddenly applied, radially expanding ring load.     

On permanent long-wave distortions of a railway track due to the moving vehicle load

Summary  The paper presents a simple mathematical model which describes the evolution of the vertical profile of a railway track caused by the load arising from moving vehicles. Owing to the fact that the track ballast is not perfectly elastic, each passage of a train is accompanied by a residual deformation of the ballast. Being very small, these deformations, however, accumulate with time. It is shown that an initial imperfection in the vertical profile of the track will either grow or diminish after each passage. For given track and vehicle, the rate of growth is determined by the characteristic length of the imperfection and by the velocity of the vehicle. Received 3 February 2000; accepted for publication 19 July 2000