DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.     

此题还一个解——对《正确使用平均值》一文的补充

《物理通报》2010年第6期一篇文章《正确使用平均值》[1]中,例题1的参考解答是利用动量与能量的观点来研究的.但笔者认为此题还有一个解,分析如下.文中如有不当之处还请各位批评指正.     

Equation of State and Elastic Constants of Compressed fcc Cu

First-principles calculations of equation of state and single-crystal elastic constants of copper are carried out up to twofold compression. The Helmholtz free energies are calculated using the quasi-harmonic phonon approach based on density-functional theory within both the local density approximation and the generalized gradient approximation （GGA）. We find that the results calculated within GGA agree better with the experimental measurements in overall. The equation of state and the zero-pressure single-crystal elastic constants are close to the experimental values.     

Young＇s modulus surface and Poisson＇s ratio curve for tetragonal crystals

This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.     

Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.     

First-principles calculations for elastic properties of rutile TiO2 under pressure

This paper studies the equilibrium structure parameters and the dependences of the elastic properties on pressure for rutile TiO2 by using the Cambridge Serial Total Energy Package （CASTEP） program in the frame of density functional theory. The obtained equilibrium structure parameters, bulk modulus B0 and its pressure derivative B′0 are in good agreement with experiments and the theoretical results. The six independent elastic constants of rutile TiO2 under pressure are theoretically investigated for the first time. It is found that, as pressure increases, the elastic constants C11, C33, C66, C12 and C13 increase, The variation of elastic constant C44 is not obvious and the anisotropy will weaken.     

铝的动态屈服强度测量及再加载弹性前驱波的形成机理分析

利用激光干涉测速技术(VISAR)测量LY12铝合金在20—34 GPa冲击压力下经历加载-卸载和加载-再加载过程的样品/窗口界面粒子速度剖面，采用AC方法确定了具有较高精度的动态屈服强度值.实验结果和文献发表的数据具有较好的一致性.通过以平面焊接方式制作组合飞片，克服了组合飞片在气炮发射过程中可能发生分离的技术困难，使铝的动态屈服强度测量压力范围从22 GPa扩展到了34 GPa.同时，根据对不同实验条件下的加载-再加载过程的比较，对再加载弹性前驱波的形成机理进行了讨论，认为位错是形成该现象的主要原因.     

金属材料再加载“准弹性”响应的实验验证

从连续介质力学理论看，当材料发生屈服后处于上屈服面，对处于上屈服面的材料进行再加载，将沿着上屈服面，依然发生塑性流动，不可能存在弹性响应。Asay则认为冲击压缩后的材料并非处于上屈服面，由此对处于冲击压缩态的材料进行卸载或再加载，可以观测到弹-塑性转变。国内部分人认为，实验观测到的弹性响应可能是LiF窗口（其冲击阻抗低于Al或其他高阻抗样品的冲击阻抗）反射的稀疏波所致。为了澄清对上述问题的观点，通过低阻抗样品的冲击实验，在消除冲击波在样品／窗口界面反射的稀疏波干扰的情况下，     

采用微分求积法分析薄板的气动弹性响应

为减轻结构重量，新一代飞行器的结构设计中更多地采用了薄壁结构，在超音速或超高音速飞行条件下，薄板的气动弹性响应相当剧烈。分析薄板的气动弹性响应方法主要有两类：第一类为经典的伽辽金方法；第二类为有限元方法。受薄板形状和边界条件的限制，伽辽金方法能够研究的问题是非常有限的，有限元方法虽然具有普适性，但本质上属于数值方法，其计算精度和收敛性必将受所选单元类型以及数值计算误差的影响。在薄板的气动弹性分析领域，文中采用一种全新的方法，即微分求积方法。     

色散作用能的推导

对两个振动频率与极化系数不同的三维振子的色散作用能给出了一种简明的推导。