双曲抛物面

There were many studies on the static properties of common types of reticulated shells, such as sphere, cylinder, elliptic paraboloid, hyperbolic paraboloid and so on, while little systematical research on ellipsoid reticulated shells has been reported by now.

摘要对于比较常见的网壳结构形式，如球壳、圆柱面网壳、椭圆抛物面网壳、双曲抛物面网壳等，其静力性能的研究已比较成熟，有关其非线性全过程分析的策略、思想及实施方法，很多学者均进行了深入的分析和探讨，但对椭球面网壳这一结构形式来说，目前还没有系统的研究。

Taking temperature variation into account, nonlinear vibration of elliptic paraboloid cable net made of carbon fiber cables was investigated under excitation of main structure displacement.

在考虑温度变化的基础上，研究椭圆平面双曲抛物面碳纤维索网在主体结构激励下的非线性振动问题。

Namely, we discrete some function surfaces including sphere, elliptic paraboloid and hyperboloid paraboloid as samples, and give the error estimation in order to compare, analyze and explain results.

我们以离散型函数曲面（包括球面，椭球面，双曲抛物面）作为样本，对各种方法的实验结果进行误差统计和分析比较。

Its nonlinear vibration equation was presented, and the approximate solution of nonlinear vibration of elliptic paraboloid cable mesh was given by using Galerkin principle and KBM method.

建立椭圆平面双曲抛物面碳纤维索网在主体结构位移激励下的非线性振动方程，采用Galerkin原理及KBM法求得椭圆平面双曲抛物面碳纤维索网非线性振动的近似解。

And the effects of foundation displacement excitation,temperature,amplitude and asexternal damping on the nonlinear vibration of elliptic paraboloid cable net with the comparison between steel cable and carbon fiber cable were discussed.At last the conclusions are obtained that the temperature have great influence on steel cable and bat not on carbon fiber cable,and the vibration characteristics of cable net using carbon fiber cables is superior to cable net using steel.

在把碳纤维索网与钢丝索网比较的基础上，讨论分析了位移激励、温度、振幅、外阻尼等因素对椭圆平面双曲抛物面碳纤维索网非线性振动的影响，得到了碳纤维索网对温度变化不敏感，而钢丝索网受温度的影响却很大，且碳纤维索网振动特性优于钢丝索网振动特性的结论。

Taking into account the temperature effect ,the nonlinear vibration of elliptic paraboloid cable net using carbon fiber cables under foundation displacement excitation was studieded.Then the nonlinear vibration equation was presented,whose approximate solution was given with Galerkin principle and KBM method.

在考虑温度变化的基础上，研究椭圆平面双曲抛物面碳纤维索网在基础激励下的非线性振动问题，建立了椭圆平面双曲抛物面碳纤维索网在基础位移激励下的非线性振动方程，采用Galerkin原理及KBM法求得了椭圆平面双曲抛物面碳纤维索网非线性振动的近似解。

The authors show that the hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

作者证实：单叶双曲面和双曲抛物面是直线曲面。

On the basis of these theories, The specific project—the hyperbolic paraboloid shell structure named Shijingshan Gymnasium is introduced, and the finite element model is established, including calculation of load, simplification of node nature and simplification of support.

在这些理论的基础上，引入工程实例——石景山体育馆双曲抛物面网壳结构，建立有限元模型，包括使用荷载的计算、节点性质的简化、支承的简化等。

We discover that under a general configuration the twist system of this mechanism belongs to the seventh special three-system, and all the twist axes are distributed on a hyperbolic paraboloid that is special and unusual and rarely studied. Under original configuration it belongs to the fourth special three-system.

我们发现：该机器人在一般位形下，它的所有运动螺旋轴线在空间分布的二次曲面是比较特殊的，罕见的，是过去理论上研究很少的双曲抛物面，属于第七种特殊三系，在起始位置时属于第四种的特殊三系。

The main research contents are stated asfollow: 1. Simplified analysis method of space grids structuresDouble-layer space grids have been assumed as sandwich plate, and are analyzed bythe nontraditional theory of plate with consideration of shear deformation and threegeneralized displacements. Using the theory of energy variation, simplified methodsfor bending, stability and vibration analysis of double-layer space grids have been putforward based upon the idea of split rigidity. The formulas for calculating internalforces, displacements, critical load and natural frequency have been given out. Set thestable cables and bearing cables in hyperbolic paraboloid cable nets are all replaced bytruss-cable to form truss-cable nets structures. Natural vibration analysis method fortruss-cable nets structures has been put forward using the energy variation method andRayleigh method.

主要内容包括： 1、空间网格结构静动力简化分析方法把网架结构简化为夹层板，采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析，基于分解刚度思想利用能量变分原理提出了网架结构弯曲、稳定与振动分析的简化计算方法，给出了位移、内力、屈曲临界荷载和固有频率的计算公式；将双曲抛物面索网中的稳定索与承重索均用劲性索代替形成劲性索网结构，基于能量变分法和Rayleigh法给出了劲性索网结构固有振动分析的简化计算公式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。