On a local energy decay estimate of solutions to the hyperbolic type Stokes equations

In this paper, we discuss a local energy decay estimate of solutions to the initial-boundary value problem for the hyperbolic type Stokes equations of incompressible fluid flow in an exterior domain and a perturbed half-space. The equations are linearized version of the hyperbolic Navier–Stokes equations introduced by Racke and Saal [15], which are obtained as a delayed case for the deformation tensor in the incompressible Navier–Stokes equations. Our proof of the local energy decay estimate is based on Dan and Shibata [2]. In [2], they treated the dissipative wave equations in an exterior domain and discussed the local energy decay estimate. Our approach uses the fact that applying the Helmholtz projection to the hyperbolic type Stokes equations, we obtain equations similar to the dissipative wave ones.     

Buckling of a Timoshenko beam on elastic foundation with uncertain input data

A monotone dependence of the critical buckling load of a simplysupported Timoshenko–Mindlin beam both on the shear correctionfactor and on the stiffness of foundation is proved. Then theworst-scenario method is employed to find the ‘most dangerous’input data.     

Boundary Properties of Second-Order Partial Derivatives of the Poisson Integral for a Half-Space ℝk+1 + (k>1)

The boundary properties of second-order partial derivatives of the Poisson integral are studied for a half-space ^k+1 ₊.     

Integration of Singularities in FE/BE Analyses of Soil-foundation Interaction with Non-homogeneous Elastic Soils

This paper addresses the derivation of the boundary integral equations for a non-homogeneous elastic half-space subjected to constant surface tractions on an arbitrarily shaped area on the basis of the respective Green's functions. The type of non-homogeneity considered is a power law variation of Young's modulus with depth below the surface of the half-space. Two different methods, a contour integral and an integration-free approach are presented, applicable for arbitrarily and rectangular shaped boundary elements, respectively. In the first one the divergence theorem is used in order to reduce the integration of a two-dimensional surface element to an integration over the element's confining boundary only. In the second approach no integration at all is needed since the solution is found simply by evaluating functions to be determined at the boundaries of the loaded rectangle.     

An antisymmetric problem of a penny-shaped crack in a piezoelectric medium

Summary  An exact, three-dimensional analysis is developed for a penny-shaped crack in an infinite transversely isotropic piezoelectric medium. The crack is assumed to be parallel to the plane of isotropy, with its faces subjected to a couple of concentrated normal forces and a couple of point electric charges that are antisymmetric with respect to the crack plane. The fundamental solution of a concentrated force and a point charge acting on the surface of a piezoelectric half-space is employed to derive the integral equations for the general boundary value problem. For the above antisymmetric crack problem, complete expressions for the elastoelectric field are obtained. A numerical calculation is finally performed to show the piezoelectric effect in piezoelectric materials. It is noted here that the present analysis is an extension of Fabrikant's theory for elasticity. Received 30 August 1999; accepted for publication 1 March 2000     

双向弹簧夹层假定的弹性地基上双层板的解

建立了轴对称条件下,层间有双向弹簧夹层的弹性地基上双层板力学模型,应用Hankel(汉克尔)变换法推演得到了任意轴对称荷载作用下的Winkler(文克勒)地基、双参数地基和弹性半空间体地基上无限大双层板的一般解析解,给出了双层板的挠度、弯矩、剪力,以及层间反力和位移的计算公式.进而,利用该力学模型的解,分析了层间条件对双层板挠度、弯矩的影响规律,计算了上、下层板的中性轴位置,讨论了层间双向弹簧系数的取值方法.结果表明:1)随着层间竖向弹簧参数增大,上层板挠度和弯曲应力减小,下层板挠度和弯曲应力增大;随着层间水平摩阻参数增大,上、下层板的挠度和弯矩均减小;2)当双层板的剪切和压缩效应系数分别取2/3,3/5时,双层板的剪切和压缩效应可较好地被考虑;3)上、下层板的中性轴位置是变化的,它随着距荷载圆中心点的距离增大而向上、下层板各自中面趋近.     

Forced vibration of curved beams on two-parameter elastic foundation

Forced vibration analysis of curved beams on two-parameter elastic foundation subjected to impulsive loads are investigated. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method. The solutions obtained are transformed to the real space using the Durbin’s numerical inverse Laplace transform method. The static and forced vibration analysis of circular beams on elastic foundation are analyzed through various examples.     

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory

In the present work, the effect of longitudinal magnetic field on wave dispersion characteristics of equivalent continuum structure (ECS) of single-walled carbon nanotubes (SWCNT) embedded in elastic medium is studied. The ECS is modelled as an Euler–Bernoulli beam. The chemical bonds between a SWCNT and the elastic medium are assumed to be formed. The elastic matrix is described by Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation. The governing equations of motion for the ECS of SWCNT under a longitudinal magnetic field are derived by considering the Lorentz magnetic force obtained from Maxwell’s relations within the frame work of nonlocal elasticity theory. The wave propagation analysis is performed using spectral analysis. The results obtained show that the velocity of flexural waves in SWCNTs increases with the increase of longitudinal magnetic field exerted on it in the frequency range; 0–20 THz. The present analysis also shows that the flexural wave dispersion in the ECS of SWCNT obtained by local and nonlocal elasticity theories differ. It is found that the nonlocality reduces the wave velocity irrespective of the presence of the magnetic field and does not influences it in the higher frequency region. Further it is found that the presence of elastic matrix introduces the frequency band gap in flexural wave mode. The band gap in the flexural wave is found to independent of strength of the longitudinal magnetic field.     

角钢插入式基础抗拔试验与分析

通过对 １１ 组 １９ 个角钢插入式基础试件的抗拔试验,得到了角钢在不同埋置长度、不同锚固形式下的抗拔承载力、角钢与混凝土间的粘结应力分布、平均粘结应力以及角钢插入式基础的破坏形式、最大试验荷载等。为工程设计提供了基础数据。     

VIBRATIONS OF STEPPED RECTANGULAR THIN PLATES ON WINKLER’S FOUNDATION

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