Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.

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 simulation 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.

Transverse Vibration Analysis of Concentrated Mass-Loaded Thin Circular Plate Based on Strcutural Circumferential Periodicity

The structural circumferential periodicity of inertial excitation produced by concentrated mass was utilized to establish the mathematical model of thin circular plate carrying eccentric concentrated mass and to analyze its transverse vibration. The fundamental frequency coefficient, natural frequency and mode shape function are determined by this method. A clamped thin circular plate was taken as an example to study the mass effect on the vibrating system.Comparison between the present results and published ones exhibits excellent agreement, which shows that the analytical method in this paper can be used to predict the transverse vibration parameters accurately.

LARGE DEFLECTION PROBLEM OF THIN ORTHOTROPIC CIRCULAR PLATE ON ELASTIC FOUNDATION WITH VARIABLE THICKNESS UNDER UNIFORM PRESSURE

Basic equations for large deflection theory of thin orthotropic circular plate on elastic foundation with variable thickness under uniform pressure are derived in this paper. The second opproximation solutions are obtained by means of the modified iteration method. The relation curves of the nondimensional loading and foe deflection, as to the differential ε and μrθ and λ are shown in Figs. 2, 3, 4. In special circumstance, the results are in accordance with those in [1], [6].

A NEW TECHNIQUE FOR SOLVING NON-AXIALLY SYMMETRICALLARGE DEFLECTION OF ELASTIC AND THIN CIRCULAR PLATES

A new technique for solving large deflection problem of circular plates flexural non-axisymmetrically is proposed in this paper. The large deflection problem of a circular plate with built-in edge under non-axisymmetrical load is taken as an example to clarify the principle and procedure of the technique mentioned here. The technique given here can also be used to solve large deflection problem of circular plates under other non-axisymmetrical loads and boundary conditions.

THE GENERAL SOLUTION FOR AXIAL SYMMETRICAL BENDING OF NONHOMOGENEOUS CIRCULAR PLATES RESTING ON AN ELASTIC FOUNDATION

In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting, on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions. The uniform convergence of the solution is proved. This general solution can also he applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

负泊松比手性结构圆薄板的参数设计

薄膜张紧在曲线边界上必然产生反枕效应,这会降低网状可展开天线的型面精度。为了减少影响,通常采用增加径向肋或者网面牵引索等措施,但这些方法会增加可展开天线的复杂程度。王一鸣、黄鹏飞提出了一种弱刚度复合膜,通过调整厚度使其具有一定的弯曲刚度降低反枕效应的影响,但厚度的增加会增加天线的质量。根据薄板的弯曲刚度方程可知,为了在不改变材料厚度的情况下改变弯曲刚度,通过调节材料的泊松比可以达到这个目的。文章利用等效法计算了伞天线反射面形成时两肋间材料需要施加的位移;将天线反射面等效为薄板,计算了在此位移下为消除反枕效应圆薄板所需的弯曲刚度;选取了合适的负泊松比结构,即手性结构,计算了为实现这一弯曲刚度所需的手性结构胞元的几何参数;最后,利用有限元对胞元进行强度校核,以保证设计的手性结构能满足后续实验加载需求。

UNSYMMETRICAL LARGE DEFORMATION PROBLEM OF ORTHOTROPIC PLATES

Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given .

ANALYTICAL FORMULAS OF SOLUTIONS OF GEOMETRICALLY NONLINEAR EQUATIONS OF AXISYMMETRIC PLATES AND SHALLOW SHELLS

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.

Investigations into sensing characteristics of circular thin-plate electrostatic sensors for gas path monitoring

Circular thin-plate electrostatic sensors are promising in gas path monitoring due to their advantages of non-intrusiveness and easy installation. The spatial sensitivity and filtering effect are two important performance parameters. In this paper, an analytically mathematical model of induced charge on a circular thin-plate electrode is first derived. Then the spatial sensitivity and filtering effect of the circular electrostatic sensor are investigated by numerical calculations. Finally,experimental studies are performed to testify the theoretical results. Both theoretical and experimental results demonstrate that circular thin-plate electrostatic sensors act as a low-pass filter in the spatial frequency domain, and both the spatial filtering effect and the temporal frequency response characteristics depend strongly on the spatial position and velocity of the charged particle. These conclusions can provide guidelines for the optimal design of circular thin-plate electrostatic sensors.

THE ELASTIC-PLASTIC BENDING AND WRINKLING OF THIN CIRCULAR PLATES

Ⅰ. INTRODUCTIONThin circular plates, a kind of the basic structural element widely used in engineering,are of the simplest plane-stress mechanical model with double curvatures. Hence, the investigation on the fundamental mechanical properties of the thin circular plates has been attracting great attention and brought about many results. Due to the difficulties

固定边界阶梯圆盘的设计及其振动特性计算

利用薄板的弯曲振动理论,推出了固定边界条件下带有一个阶梯的阶梯圆盘的频率方程,提出了求解频率方程的数值计算方法,编制了计算程序,由此可计算出阶梯圆盘的半径和节线位置,设计出完整的阶梯圆盘。并用有限元仿真软件对阶梯圆盘的振型和位移分布进行了计算,两者计算结果基本吻合,为这种条件下阶梯圆盘的设计提供了方法。

正交各向异性板的非对称大变形问题

从各向异性板的基本理论出发 ,推导出正交各向异性圆板的非对称大变形基本方程 ,利用Fourier级数把问题的偏微分方程转化为一组可积分求解的非线性常微分方程 ,并给出利用迭代法求解该问题的基本方法·

弹性圆薄板在随动力作用下的屈曲问题分析

取弹性圆薄板内一微元体,建立了圆板在非保守载荷切向均布随动力作用下的轴对称非线性控制方程,考虑周边固支和周边不可移简支两种边界条件,采用打靶法和解析延拓法求解了所得两点边值问题,获得了圆薄板特征值问题的数值解,结果可供工程设计时参考使用.

不同孔隙度中心受压圆形薄板试样渗透特性试验研究

通过控制砂粒粗细的方法自制不同孔隙度的圆形薄板试样,利用RSM-SY7基桩多跨孔超声波自动循测仪测量其孔隙度值并进行标记。利用自主研发的渗透试验装置,在DDL600电子万能试验机上进行中心受压圆形薄板试样弯曲变形过程中的渗透特性试验;研究孔隙度对圆形薄板试样轴向抗压强度、初始渗透率的影响及其对圆形薄板试样弯曲变形过程中轴向载荷与渗流量出现峰值时间差的影响,并研究圆形薄板试样弯曲变形过程中渗透率的变化规律。研究结果表明:不同孔隙度中心受压圆形薄板试样弯曲变形过程中,其渗透率均在整体上呈现先增大后减小的趋势;试样的孔隙度越大,其轴向载荷峰值Fmax、初始渗透率整体越趋于减小;当试样孔隙度较大时,其弯曲变形过程中轴向载荷F峰值先于流量Q峰值出现,反之,其流量Q峰值先于轴向载荷F峰值出现。

中心带有弹性安置质量的圆板横向振动的有限元分析

本文用三节点环形有限元计算了中心带有弹性安置质量的薄圆板轴对称自由振动的频率,给出了各种边界条件及各种质量比、刚度比的频率参数,并分析了附加弹簧质量对系统固有频率的影响。计算结果与现有文献的结果作了对比,证明本文的方法具有很高的精度,所得频率参数有5位以上的有效数字。

偏心冲击荷载作用下薄圆板动力学响应的保结构分析

关注动力学系统的局部几何性质,采用多辛分析方法研究了偏心冲击荷载作用下薄圆板振动特性.在探索偏心冲击荷载作用下薄圆板振动问题动力学控制方程的对称性和守恒律的对应关系基础上,对动力学控制方程在多辛体系下重新描述,并采用显式中点差分离散方法构造其多辛格式,通过对存在不同相对偏心距冲击荷载作用下的薄圆板振动过程的数值模拟,研究了相对偏心距对薄圆板振动特性的影响,同时,数值模拟结果也充分体现了多辛算法的良好保结构性能.该研究结果不仅为由于荷载作用位置误差带来的动力学响应偏差估计提供了依据,而且为偏心冲击动力学问题的研究提供了新的途径.

热力联合作用弹性薄圆板的弯曲与屈曲

导出了热力联合作用下弹性薄圆板的弯曲动力响应控制方程，讨论了其弯曲变形特点及影响失效的因素。分析表明在短时热能沉积作用下，热屈曲是弹性薄板失效的主要方式之一；反鼓包或反冲塞是热屈曲的后继行为；增加外载和热能沉积功率水平都将加速热屈曲的发生；材料的温度相关性与热能沉积的时空分布对薄板的力学行为都有重要影响，同为产生和影响热剪切失效（反冲塞）的重要因素。

非轴对称载荷作用下弹性圆形薄板弯曲分析

以Airy应力函数为未知量的板内平面问题和以挠度为未知量的薄板弯曲问题都可归为双调和方程边值问题,二者具有相似性。根据圆内双调和问题自然边界归化后的Poisson积分式,得到圆板内平面问题Airy应力函数以及弯曲问题挠度的边界积分公式,由积分公式对简单边值问题直接积分可得到解析解。对非轴对称问题简支圆板,利用固支圆板作为基本体系,应用功的互等定理对其进行求解。结果表明:本方法简单、直观、精度高。

简支圆薄板在机械场与电磁场耦合作用下的分岔与混沌

研究了机械场与电磁场耦合作用下简支圆薄板的分岔与混沌问题。在给出圆薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上,得到了横向稳恒磁场、环向电流和载荷共同作用下圆薄板的振动方程,并采用四阶Runge-Kutta法求解方程。通过变化机械载荷频率使系统由周期状态进入混沌状态,并且由分岔图与Lyaponov指数图来判定系统是否进入混沌状态;给出了相应的位移波形图,相平面轨迹及庞加莱截面;讨论了磁场与电流对系统运动状态的影响。