Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids

Many composite materials, including biological tissues, are modeled as non-linear elastic materials reinforced with elastic fibers. In the current paper, the full set of dynamic equations for finite deformations of incompressible hyperelastic solids containing a single fiber family are considered. Finite-amplitude wave propagation ansätze compatible with the incompressibility condition are employed for a generic fiber family orientation. Corresponding non-linear and linear wave equations are derived. It is shown that for a certain class of constitutive relations, the fiber contribution vanishes when the displacement is independent of the fiber direction.Point symmetries of the derived wave models are classified with respect to the material parameters and the angle between the fibers and the wave propagation direction. For planar shear waves in materials with a strong fiber contribution, a special wave propagation direction is found for which the non-linear wave equations admit an additional symmetry group. Examples of exact time-dependent solutions are provided in several physical situations, including the evolution of pre-strained configurations and traveling waves.     

悬链线竖向集中力作用下的构形分析和张力计算

目前,悬链线在竖向集中力和均布荷载共同作用下的构形分析和受力计算的理论仍不完善。针对这一问题,通过引入悬链线的几何约束方程、力平衡方程和超越方程,建立了竖向集中力与均布荷载共同作用下的非线性方程组。采用牛顿迭代法求解方程组,得到了悬链线的构形和受力情况。为了验证理论计算的正确性,进行了算例和试验验证。结果表明,算例的计算结果与文献结论保持一致,试验测得的构形和水平张力大小与理论计算的构形和水平张力大小吻合较好。本文的理论计算可以更加简单精确地计算出悬链线在竖向集中力和均布荷载共同作用下的构形和受力情况,为实际工程提供重要的理论指导。     

Electric field induced non-linear multisubband electron mobility in V-shaped asymmetric double quantum well structure

ABSTRACT

We study the effect of the external electric field F_ext on the low-temperature electron mobility μ in an asymmetrically doped Al_xGa_1-xAs based V-shaped double quantum well (VDQW) structure. We show that nonlinearity of µ occurs under double subband occupancy on account of intersubband effects. The field F_ext alters the VDQW potential leading to transfer of subband wave functions between the wells, which affects the scattering potentials and hence μ. In the VDQW structure, due to the alloy channel layer, the alloy disorder (Al-) scattering happens to be significant along with the ionised impurity (Imp-) scattering. The non-linear behaviour of μ is because of μ^Imp, while the overall magnitude of μ is mostly due to μ^Al. The increase of difference in the doping concentrations of the outer barriers increases the nonlinearity of μ. The oscillatory character of μ is amended by varying the width of the well and barrier and also the height of the VDQW. Our results can be used to study VDQW based nanoscale field effect transistor structures.     

有应力史差非匀质截面轴心受压杆的性能研究

对有应力史差、非匀质、非线弹性的轴心受压构件进行了理论分析和试验研究，初步揭示了此类构件的受力特点．理论分析和试验表明：此类构件截面承载力不是各部分材料承载力的简单叠加；承载力和截面破坏控制点因截面上材料的本构关系的变化和应力史差而发生改变．     

飞机风挡结构抗鸟撞一体化设计技术研究

结合大型非线性有限元分析软件，实践了飞机风挡结构由初步设计、数值仿真以及实验验证的一体化设计过程，建立了适于风挡结构材料的非线性黏弹性本构计算接口程序，对合理选取单元类型、材料模型、边界条件影响以及试验设计等工作细节进行了深入研究，通过实验与仿真计算结果的对比，验证了数值仿真计算模型的精度．为飞机风挡的抗鸟撞结构设计-数值仿真-实验验证一体化技术提供了支持论证．     

Some studies on rotors with polynomial type non-linear external and internal damping

Non-linear internal damping in rotating cylindrical shafts leads to isotropic non-linear circulatory and dissipative force fields. Orbital instability in such class of systems arises when the regenerative work due to circulatory forces exceeds the dissipative work done over an orbit. In this paper, stability condition for rotor shafts with polynomial type non-linear internal damping is derived and also it is shown that distortion of the critical orbit, which results in larger change in orbital path as compared to the change in enclosed area, may lead to stable orbit at normally unstable operating conditions. This principle is applied to stabilize a simple rotor with discontinuous stiffness characteristics, which come into effect on exceeding some threshold displacement of the rotor itself.     

A Second-Order Solution of Saint-Venant's Problem for a Piezoelectric Circular Bar Using Signorini's Perturbation Method

We study electromechanical deformations of a homogeneous transversely isotropic piezoelectric prismatic circular bar loaded only at the end faces. The constitutive relations for the material of the bar are taken to be quadratic in the displacement gradients and the electric field. It is found that the two end faces of the bar when twisted with no electric charge applied to them will exhibit a difference in the electric potential. Thus the piezoelectric cylinder could be used to measure the torque or the angular twist. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nonlinear analysis of a structure loaded by a stochastic excitation

For a non-linear system excited by a stochastic load which is expressed as a time series,a recursive method based on the Z-transform is presented.To identify the obtained response time series,a discrete wavelet transform (DWT) technique is proposed.     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。