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1.
对分离式霍普金森压杆(split Hopkinson pressure bar, SHPB) 实验中试件的黏弹性波传播的控制方程组进行Laplace 变换,并结合恰当的初始-边界条件求解,得到变换域的应力、速度、应变等变量的像函数的精确表达式. 采用该方法处理SHPB 实验中涉及黏弹性试件内部应力非均匀性问题,并给出数值反变换解. 作为特例,对于弹性试件分别采用级数展开法和留数定理进行反Laplace 变换,从而给出弹性夹层介质中应力波传播问题的解析解. 相似文献
2.
对分离式霍普金森压杆(split Hopkinson pressure bar, SHPB) 实验中试件的黏弹性波传播的控制方程组进行Laplace 变换,并结合恰当的初始-边界条件求解,得到变换域的应力、速度、应变等变量的像函数的精确表达式. 采用该方法处理SHPB 实验中涉及黏弹性试件内部应力非均匀性问题,并给出数值反变换解. 作为特例,对于弹性试件分别采用级数展开法和留数定理进行反Laplace 变换,从而给出弹性夹层介质中应力波传播问题的解析解. 相似文献
3.
A. V. Netrebko 《Mechanics of Solids》2013,48(4):473-481
The Laplace transform with respect to time is used to study the problem of loading wave propagation in a composite elastic structure modeling a split Hopkinson pressure bar. Experiments were performed to compare the theoretical and experimental results. The obtained results can be used as a basis for justifying the split Hopkinson pressure bar technique. 相似文献
4.
V. D. Kubenko 《Mechanics of Solids》2011,46(2):256-265
The problem of unsteady deformation of an elastic half-plane is considered whose surface is impacted, at an initial instant,
by a blunt-nosed rigid body, which generates diverging unsteady elastic waves and deforms the medium. The corresponding initial-boundary-value
problem is formulated whose solution is constructed for the early stage of the interaction. The integral Laplace transform
in the time variable and the integral Fourier transform in the one of the spatial variables are used. The solution of the
problem is obtained in terms of the transforms and a formal solution is constructed in terms of the original functions. For
a body with a fixed contact region, an analytical expression of the normal stress at an arbitrary point of the half-plane
as a function of time is obtained. For a body shaped as an obtuse-angled wedge, analytical expressions of the normal stress
and displacement at an arbitrary point at the symmetry axis of the problem are obtained. Calculations are performed and used
to analyze the characteristic features of the wave processes in the medium as functions of time, the surface distance, and
the mechanical properties of the material. 相似文献
5.
S. G. Pshenichnov 《Mechanics of Solids》2013,48(1):68-78
Dynamic problems describing transient wave processes in linearly viscoelastic solids are considered for bounded domains of perturbation propagation and bounded creep of the material. The integral Laplace transform with respect to time is applied to the original problem, and several statements about the properties of Laplace transforms simplifying the construction of the original functions are stated. Relations establishing a correspondence between relaxation kernels that belong to various function classes but nevertheless affect the transient processes in a similar way are proposed. The results justifying these relations in a certain range of the input data are presented. 相似文献
6.
Propagation of discontinuities in electromagneto generalized thermoelasticity in cylindrical regions
In this work we study wave propagation for a problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Wave propagation in the elastic medium and in the free space, bounding it, is investigated. 相似文献
7.
We consider a plane problem of propagation of unsteady waves in a plane layer of constant thickness filled with a homogeneous
linearly elastic isotropic medium in the absence of mass forces and with zero initial conditions. We assume that, on one of
the layer boundaries, the normal stresses are given in the form of the Dirac delta function, the tangential stresses are zero,
and the second boundary is rigidly fixed. The problem is solved by using the Laplace transform with respect to time and the
Fourier transform with respect to the longitudinal coordinate. The normal displacements at an arbitrary point are obtained
in the form of finite sums. 相似文献
8.
A fundamental solution for an infinite elastic medium containing a penny-shaped crack subjected to dynamic torsional surface tractions is attempted. A double Laplace–Hankel integral transform with respect to time and space is applied both to motion equation and boundary conditions yielding dual integral equations. The solution of the derived dual integral equations is based on an analytic procedure using theorems of Bessel functions and ordinary differential equations. The dynamic displacements’ field is obtained by inversion of the corresponding Laplace–Hankel transformed variable. Results of a representative example for a crack subjected to pulse surface tractions are obtained and discussed. 相似文献
9.
Reflection characteristics of longitudinal strain waves in a semi-infinite elastic rod con-nected to a viscoelastic stratum are investigated analytically.The three-dimensional viscoelasticity the-ory is applied to the stratum,and the Laplace transform with respect to time and the numerical inverseLaplace transform by means of Laguerre function are used.The time histories for the longitudinalstrain of an arbitrary point of the rod are presented.Two typical viscoelastic models are considered,one is the usual Maxwell-Voigt model,the other is whose relaxation function is given by a power law.The numerical results for the two models are presented and compared each other and also with previ-ously published results for the elastic stratum. 相似文献
10.
基于分数阶广义热弹性理论,针对实心球体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析. 利用热冲击的瞬时特征,借助于Laplace 正、反变换技术及柱函数的渐进性质,推导了热冲击作用周期内位移场、温度场和应力场的渐进表达式. 通过计算,得到了不同传热能力下受热冲击作用时热波、热弹性的传播规律以及位移场、温度场及应力场的分布规律. 结果表明:分数阶参数取值的不同,热波、热弹性波的传播以及各物理场的分布均有所不同,分数阶参数可视为延迟时间的影响因子,通过改变延迟效应对热弹性行为的影响来改变热冲击的作用效果. 相似文献
11.
M. I. A. Othman 《Journal of Applied Mechanics and Technical Physics》2011,52(4):644-656
A two-dimensional equation of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with the
elastic modulus dependent on temperature and with an internal heat source is established using a Laplace transform in time
and a Fourier transform in the space variable. The problem for the transforms is solved in the space of states. The problem
of heating of the upper and the lower surface of a plate of great thickness by an exponential time law is considered. Expressions
for displacements, temperature, and stresses are obtained in the transform domain. The inverse transform is obtained using
a numerical method. Results of solving the problem are presented in graphical form. Comparisons are made with the results
predicted by the coupled theory and with the case of temperature independence of the elastic modulus. 相似文献
12.
饱和土与衬砌动力相互作用的圆柱形孔洞内源问题解答 总被引:2,自引:1,他引:1
考虑饱和土与衬砌结构的动力相互作用,该文研究了内源荷载作用下圆柱形孔洞的动力响应问题.将饱和土体和衬砌结构分别视为流固耦合介质和弹性均匀介质,通过引入势函数将位移控制方程化为二维轴对称波动方程.采用拉普拉斯变换,得到饱和土体位移应力的表达式及衬砌的位移应力的表达式.利用土体与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,确定表达式的未知系数.采用逆拉普拉斯变换的数值方法,给出了问题的数值解.分析了饱和土中圆形衬砌结构随土体和衬砌结构参数变化的动力响应规律. 相似文献
13.
In this work, the generalized thermoelastic solutions with bounded boundaries for the transient shock problem are proposed by an asymptotic method. The governing equations are taken in the context of the generalized thermoelasticity with one relaxation time (L–S theory). The general solutions for any set of boundary conditions are obtained in the physical domain by the Laplace transform techniques. The corresponding asymptotic solutions for a thin plate with finite thickness, subjected to different sudden temperature rises in its two boundaries, are obtained by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, two specific problems with different boundary conditions have been conducted. The distributions of displacement, temperature and stresses, as well as the propagations, intersections and reflections of two elastic waves, named as thermoelastic wave and thermal wave separately, are obtained and plotted. These results are agreed with the results obtained in the existing literatures. 相似文献
14.
利用 Laplace 变换确定双层厚壁长圆筒的轴对称界面碰撞压力 总被引:1,自引:0,他引:1
利用Laplace变换,考虑轴对称弹性波的影响,采用特征函数展开法求解双层厚壁长圆筒受爆炸载荷作用下的轴对称弹性碰撞冲击问题,着重研究前几次碰撞冲击引起的轴对称界面碰撞压力。并对轴对称界面碰撞压力与间隙量、爆炸载荷幅值、爆炸载荷衰减系数之间的关系以及相关的动力响应作了初步的分析。 相似文献
15.
A. V. Zemskov D. V. Tarlakovskii 《Journal of Applied Mechanics and Technical Physics》2015,56(6):1023-1030
A locally equilibrium model of mechanodiffusion which comprises a coupled system of motion equations for an elastic body and a mass transfer equation is used to solve the two-dimensional nonstationary problem of elastic diffusion for an isotropic one-component layer. The solution is constructed using Fourier series, Laplace time transforms, and Fourier transforms for the spatial coordinate. The Laplace transform originals are found analytically, and the Fourier transforms are inverted by quadrature formulas. 相似文献
16.
A dynamic problem for two equal rectangular cracks in an infinite elastic plate is considered. The two cracks are placed perpendicular to the plane surfaces of the plate. An incoming shock tensile stress is returned by the cracks. In the Laplace transform domain, the boundary conditions at the two sides of the plate are satisfied using the Fourier transform technique. The mixed boundary conditions are reduced to dual integral equations. Crack displacement is expanded in a series of functions which are zero outside of the cracks. The unknown coefficients in the series are determined by the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted using a numerical method. 相似文献
17.
18.
Interaction of plane nonstationary waves with a thin elastic inclusion under smooth contact conditions 总被引:1,自引:0,他引:1
We solve the problem of determining the stress state near a thin elastic inclusion in the form of a strip of finite width
in an unbounded elastic body (matrix) with plane nonstationary waves propagating through it and with the forces exerted by
the ambient medium taken into account. We assume that the matrix is in the plane strain state, and the smooth contact conditions
are realized on both sides of the inclusion. The method for solving this problem consists in using the integral Laplace transform
with respect to time and in representing the stress and displacement images in terms of the discontinuous solution of Lamé
equations in the case of plane strain. As a result, the initial problem is reduced to a system of singular integral equations
for the transforms of the unknown stress and displacement jumps. To invert the Laplace transform, we use a numerical method
based on replacing the Mellin integral by the Fourier series. As a result, we obtain approximate formulas for calculating
the stress intensity factors (SIF) for the inclusion, which are used to study the SIF time-dependence and its influence on
the values of the inclusion rigidity. We also studied the possibility of considering the inclusions of higher rigidity as
absolutely rigid inclusions. 相似文献
19.
L. M. Brock 《Journal of Elasticity》1981,11(2):187-195
The wave propagation problem for a largely arbitrary anti-plane displacement discontinuity imposed along a line perpendicular to the surface of a stress-free linearly viscoelastic half-plane is considered. The general Laplace transform solution is obtained and then inverted for the case of a screw dislocation moving at an arbitrary speed in a Maxwell material. It is shown that the material viscoelasticity alters the coefficient of the dislocation edge stress singularity and damps the surface displacements from the elastic values. The surface damping increases with time, distance from the dislocation path and dislocation speed, whether sub- or supersonic. 相似文献
20.
粘性阻尼土中变截面桩的纵向振动特性与应用研究 总被引:2,自引:0,他引:2
考虑土体轴对称波动效应,对变截面桩在任意激振力作用下的纵向振动特性进行了研究。假定桩为竖直、弹性、变截面体,土为线性粘弹性体,其材料阻尼为粘性阻尼。利用拉普拉斯变换,将定解问题转化到拉普拉斯域内求解,通过引入势函数并结合阻抗函数的传递性,得到了拉普拉斯域内的桩顶阻抗函数解析解,进而可得到频域内的桩顶阻抗函数和速度导纳的解析解,利用卷积定理和傅里叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。基于所得解对桩的纵向振动特性进行了分析,重点讨论了桩身截面变化情况对速度导纳曲线和反射波曲线的影响,得到了许多重要结论。 相似文献