Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.     

梁长对移动荷载下梁响应影响研究

本文研究了梁跨长对移动荷载下梁稳态响应的影响.在以往的研究中,通常采用Galerkin方法或者有限元方法计算不同长度的梁的动力响应.当梁长的增加不再明显改变梁的动力响应时,可认为梁此时的长度可以代替无穷长时的情况.采用上述方法的研究表明,当梁长大于10 m时,就可以用有限长梁近似无限长梁的响应.本文通过求解有限长梁和无...     

Transient vibrations of a tau inclined cable with a riding accelerating mass

The objective of this paper is a theoretical and numerical study of the dynamics of a taut inclined cable with a riding accolerating mass, which is suspended from two points of different elevation. The moving mass is a trolley that is accelerated by a solid fuel rocket down the inclined cable and is aerodynamically brought to a halt. The thrust of the rocket is tangential to the deformed configuration of the cable.Methods of analysis consist of the dynamics of small deformations superimposed on the static catenary state. The problem is nonlinear due to presence of friction and the convective acceleration interaction of the moving mass and the cable. Galerkin's procedure for removal of spatial dependence and numerical integration are used to obtain convergent solutions.Deceased     

DYNAMIC RESPONSE OF A DOUBLE-LAYERED SUBGRADE WITH ROCK SUBSTRATUM TO A MOVING POINT LOAD

In this paper, an analytical solution for the dynamic response of a double-layered subgrade with rock substratum to a moving point load is derived. The subgrade profile is divided into two layers. The upper layer is modeled by an elastic medium and the lower layer by a fully saturated poroelastic medium governed by Biot’s theory. In the meanwhile, the subgrade is resting on the rock substratum. The analytical solutions for stress, displacement and pore pressure are derived by using the Fourier transform. Numerical results obtained by using the inverse fast Fourier transform (IFFT) are used to analyze the influence of the moving load velocity, the thickness of an elastic medium layer and a fully saturated poroelastic medium layer on the dynamic response.     

Wave propagation in liquid-saturated porous solid with micropolar elastic skelton at boundary surface

The present study is concerned with the reflection and transmission of plane waves at an interface between homogenous invisicid liquid half space and a micropolar liquid-saturated porous solid half space. The reflection and transmission coefficients of various reflected and transmitted waves with the angle of incident have been obtained. Numerical calculation has been performed for amplitude ratios of various reflected and transmitted waves. Micropolarity and porosity effects on the reflection and transmission coefficients have been depicted graphically. Some particular cases have been deduced from the present formulation.     

正交各向异性地基平面问题动力响应研究

以位移分量为基本未知量,在直角坐标系下建立正交各向异性地基的平面应变问题动力偏微分方程．采用Laplace-Fourier变换和逆变换方法,引入初始条件和边界条件,推导了任意形式表面动荷载作用下正交各向异性地基平面问题在时域内动力反应的积分形式解．基于理论解,编制了相应的计算程序,并对正交各向异性土
体表面作用线性移动谐振荷载进行了算例分析,研究了土体参数、荷载移动速度、荷载频率不同而导致的土体表面各点竖向位移幅值的变化规律,以及荷载速度对竖向应力分量的影响规律．数值分析结果表明：土体的各向异性、荷载频率和移动速度对表面位移幅值有较大影响,土体阻尼比对于荷载中心点附近的位移幅值影响较小;荷载移动速度对于竖向应力分量有较大影响,这对工程实践具有重要指导意义．     

An explicit time domain solution for ground stratum response to harmonic moving load

Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi–analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier–Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.The project is partially supported by the National Natural Science Foundation of China (50538010). The English text was polished by Yunming Chen.     

GN理论下受到移动内热源的半空间问题的研究

运用无能量耗散的热弹性GN理论研究了受到移动内热源的半空间问题.通过势函数法使问题 转化成一组偏微分方程,采用Laplace变换和Fourier变换法得到问题在变换域内表面位移 精确解. 运用级数展开法得到在小时间范围内表面位移的近似解.给出近似解的适用范围,同时给出热 源固定不动和非耦合理论下问题的解.并对铜介质进行了数值计算.     

Two-dimensional magneto-thermoelastic interactions in a micropolar functionally graded solid

Abstract

The present work is concerned with the 2D deformation in a nonhomogeneous, isotropic, micropolar, magneto-thermoelastic medium in the context of Lord-Shulman theory as a result of an inclined load. The inclined load is supposed to be a linear combination of normal load and tangential load. Material properties are assumed to be graded in x-direction. Normal mode technique is proposed to obtain the analytical expressions for the temperature field, displacement components, and stresses. These are also calculated numerically and depicted graphically to observe the variations of the considered physical variables.

Communicated by Seonho Cho.     

A fast algorithm for soil dynamics calculations by wavelet decomposition

Summary The article presents a fast numerical algorithm for calculating the response of a halfspace under any surface loads. Under certain conditions there exists an analytical solution to the problem in the Fourier domain. To get the desired response, a numerical inverse Fourier transform of this analytic solution has to be made. By using a wavelet decomposition, the proposed algorithm can reduce the calculation time significantly, thus allowing the computation of complex problems. As an example, the response of the beam-halfspace coupled system under moving load is presented. Received 6 March 1997; accepted for publication 20 May 1997     

受移动简谐力作用的多孔弹性半平面问题

研究了匀速移动的振动荷载作用下半无限多孔饱和固体中产生的应力和孔隙水压力.应用Fourier 变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和固体中应力与孔隙水压力的影响,并与相应的弹性介质的解答进行了比较.结果显示多孔饱和半平面中应力和孔隙水压力随荷载的移动速度与振动频率的增加而增大,多孔饱和固体在移动荷载下的动力响应与相应的单相弹性固体的动力响应有较大的差别.     

Two-dimensional interactions due to moving load in generalized thermoelastic solid with diffusion

The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.     

Numerical solution of the problem of motion of a load on a cracked ice sheet

A mathematical model is constructed for the motion of a load on a cracked ice sheet. Examples of calculation of ice deflections are given, and the calculation results are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 151–156, May–June, 2008.     

桥梁结构移动平稳随机荷载识别新方法

移动的平稳随机荷载对简支梁的作用,相当于固定的调制函数已知的非平稳随机荷载对简支梁结构的作用.本文以此为基础,研究了移动平稳随机荷载的识别问题.首先基于虚拟激励法的思想,利用特征值分解及奇异值分解技术,由虚拟位移响应反演虚拟广义坐标,有效地避免了矩阵求逆,得到高精度的广义坐标谱;同时利用Wiener-Khintchine关系及Duhamel积分,由广义坐标谱值反演得到平稳随机激励谱密度.仿真算例表明,只要适当地选取参振振型及测点位置,本文方法可以有效地识别桥梁结构的移动平稳随机荷载.     

Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.     

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。     

Moving least squares reconstruction for sharp interface immersed boundary methods

We propose a new approach for reconstructing velocity boundary conditions in sharp-inerface immersed boundary (IB) methods based on the moving least squares (MLS) interpolation method. The MLS is employed to not only reconstruct velocity boundary conditions but also to calculate the pressure and velocity gradients in the vicinity of the immersed body, which are required in fluid structure interaction problems to obtain the force exerted by the fluid on the structure. To extend the method to arbitrarily complex geometries with nonconvex shaped boundaries, the visibility method is combined with the MLS method. The performance of the proposed curvilinear IB MLS (CURVIB-MLS) is demonstrated by systematic grid-refinement studies for two- and three-dimensional tests and compared with the standard CURVIB method employing standard wall-normal interpolation for reconstructing boundary conditions. The test problems are flow in a lid-driven cavity with a sphere, uniform flow over a sphere, flow on a NACA0018 airfoil at incidence, and vortex-induced vibration of an elastically-mounted cylinder. We show that the CURVIB-MLS formulation yields a method that is easier to implement in complex geometries and exhibits higher accuracy and rate of convergence relative to the standard CURVIB method. The MLS approach is also shown to dramatically improve the accuracy of calculating the pressure and viscous forces imparted by the flow on the body and improve the overall accuracy of FSI simulations. Finally, the CURVIB-MLS approach is able to qualitatively capture on relatively coarse grids important features of complex separated flows that the standard CURVIB method is able to capture only on finer grids.     

Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

An analytic solution is obtained to describe the vibrations and dissipative heating of a simply supported infinite cylindrical panel under periodic normal loads moving over its surface with a constant velocity. Special attention is focused on resonant vibrations, which result in the most intensive dissipative heating. It is additionally assumed that the material of the panel is viscoelastic, its properties are independent of temperature, and Poisson’s ratio is real. The influence of thickness, radius of curvature, load velocity, and viscoelastic properties on the thermal state of the panel is analysed against the thermal state of the plate__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 100–109, April 2005.     

Vibrations and Dissipative Heating of a Viscoelastic Beam under a Moving Load

The vibrations and dissipative heating of an infinite viscoelastic beam under a moving load are studied on the basis of Timoshenko beam theory. The influence of transverse-shear strain and rotary inertia on the critical velocities of the moving load, the amplitude of bending vibration, and the temperature of dissipative heating is analyzed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 69–76, January 2005.     

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