ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ     

静载荷作用下柔韧圆板的大幅度振动

本文首先给出了均布载荷作用下柔韧圆板的大幅度振动方程，按文中给出的时间模态假设导了该问题的非线性耦合的代数和微分特征方程组，利用修正迭代法求出了该方程组的近似解析解，得到了柔韧圆振动的幅频－载荷特征关系，讨论了静载荷对其振动性态的影响。     

圆柱绕流的非线性动力学

本文利用非线性动力学的概念和方法来研究粘性不可压缩流体的二维圆柱绕流问题．计算了定常流失稳以及出现混沌的临界雷诺数，并估计了混沌解的一些统计特征．     

压电激励圆形曲梁的静态响应及位移控制

研究压电激励圆形曲梁的静态位移响应及位移控制的参数特性。将压电夹层圆形曲梁等效为单层结构,基于一维小曲率曲梁理论,建立其控制方程。在集中弯矩和径向集中力以及电载荷作用下,分析了带压电激励器的圆形悬臂曲梁的静态响应。与有限元结果比较表明:本文的理论模型能够模拟压电激励的小曲率圆形曲梁的静态响应。压电夹层圆形曲梁在任意位置的径向集中力载荷作用下,控制其自由端径向位移响应为零,求得控制电压的解析表达,数值分析表明:随着集中力载荷的位置变化和梁长的变化,最优控制电压将出现峰值和反号。     

ANALYTICAL EVALUATION OF PERMANENT DEFLECTION OF A THIN CIRCULAR PLATE STRUCK NORMALLY AT ITS CENTER BY A PROJECTILE

The permanent deflection of a thin circular plate struck normally at its center by a projectile is studied by an approximate theoretical analysis,FEM simulation and experiment.The plate made of rate sensitive and strain-hardening material undergoes serious local deformation but is not perforated during the impact.The theoretical analysis is based on an energy approach, in which the Cowper-Symonds equation is used for the consideration of strain rate sensitive effects and the parameters involved are determined with the aid of experimental data.The maximum permanent deflections predicted by the theoretical model are compared with those of FEM sim- ulation and published papers obtained both by theory and experiment,and good agreement is achieved for a wide range of thickness of the plates and initial impact velocities.     

SCATTERING OF CIRCULAR CAVITY IN RIGHT-ANGLE PLANAR SPACE TO STEADY SH-WAVE

Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the method introduced here.     

Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians

We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables.     

Natural Vibrations of a Cylindrical Shell with Circular Ribs Attached by Means of Discrete Elastic Elements

The vibrations of a cylindrical shell reinforced with circular ribs attached to it by means of discrete elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modeled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 108–113, October 2005.     

An investigation of meterial properties of non-homogeneous cylindrically orthotropic circular plates

It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this paper is to verify the effect of radius on the materal properties According to the flat stress-strain relation the values of material properties E_r E_a and v_θr which are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.     

STABILITY OF CIRCULAR RING OF CIRCULAR CROSS-SECTION UNDER UNIFORMLY DISTRIBUTED TORSION 1)

圆环在均布扭力矩作用下的变形特殊且容易发生跳跃,不考虑稳定性而得到的一些结论将可能不存在。本文利用最小势能原理导出圆截面圆环在均布扭力矩作用下的平衡路径,并根据系统稳定性的能量判据,对圆环的平衡稳定性、变形与运动过程进行分析,最后得到稳定平衡状态下圆环横截面上的内力最大值。