Nonlinear dynamics of cable nets

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本课程《索网非线性动力学》是结构动力学领域一门高级课程,旨在探索索结构的非线性动力学行为。 **课程概述:** 索结构,从船帆到悬索桥,在结构工程领域占据重要地位,因其轻巧优雅而吸引建筑师的目光。预应力膜、气承、充气或张力结构、悬索桥、斜拉桥、天线或拉线桅杆、海事应用、雪崩网、落石防护网、起重机、帆船、系泊缆、拖网、浮动或沉没防波堤、浮空器,乃至雨伞、晾衣绳等日常物品,都属于索结构的范畴。这些结构由纯受拉构件组成,其最终形态受荷载和初始预应力影响。与无载几何形状相比,它们会发生大变形,这也会影响其刚度。因此,此类结构的分析必须考虑非线性,即针对每种荷载组合,同时考虑大变形,此时叠加原理不再适用。 特别是索网,如双曲抛物面形状的索网,属于索结构家族,能够覆盖大跨度区域而无需中间支撑,并能承受远超自身重量的荷载,是建造机库、体育场、游泳池、冰球场、展览馆、剧院、音乐厅、教堂等大跨度空间的理想解决方案。 **课程定位:** 这是一门高级动力学课程,要求学员具备扎实的结构线性动力学理论知识。本课程将为学员打开索结构非线性动力学这一非凡世界的大门。尽管工程师们熟悉线性动力学,但索结构非线性动力学行为隐藏着许多难以察觉的新颖且不同的共振现象,本课程将与学员一同探索和揭示这些现象。

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From the ship sails to the suspension bridges, tensile structures have conquered the field of structural engineering, triggering also the interest of architects with their lightness and elegancy. Prestressed membranes or cable roofs, air-supported, inflated or tensegrity structures, suspension or cable-stayed bridges, antennae or guyed masts, sea-based applications, smaller structures such as snow avalanche nets, rock fall barriers, cranes, sailboats, mooring lines, trawl lines and nets, floating or submerged breakwaters, aerostats, or even simpler creations, such as the umbrellas or the rope we use to dry the laundry, belong to the family of tensile structures. They consist of members that operate in pure tension. Their final shape depends on the loads and the initial pretension. They present large deformations with respect to the unloaded geometry, which influences also their stiffness. The analysis of such structures should be nonlinear for each load combination, considering large deformations, while the principle of superposition does not apply.Cable nets, forming the surface of a hyperbolic paraboloid belong to this family of tensile structures. They have the capacity to cover large spans without intermediate supports and to carry loads much heavier than their own weight. They are attractive solutions for covering hangars, stadia, swimming pools, ice rinks, exhibition halls, theatres, concert halls, churches and other long-span areas.This is an advanced course in dynamics, which requires a good knowledge of the theory of linear dynamics of structures. It constitutes a window to the extraordinary world of cable nonlinear dynamics. Although engineers are familiar with the science of linear dynamics, the nonlinear dynamic behaviour of tensile structures hides several new and different resonant phenomena, difficult to be detected. Let us discover them together.

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