A model for the non-linear dynamic behaviour of pre-stressed cable trusses is presented. The model provides the basis for a simplified description of the (in-plane) non-linear dynamical behaviour of biconcave and bi-convex cable structures (as well as of single cables) subject to different loading (and mass distribution) conditions. The simplicity of the proposed approach is coupled with its ability to schematically represent a wide range of actual structures, including light pedestrian suspended cable bridges and cable roofs with vertical harnesses, under different vertical loading conditions. Although aiming at the needs of the practitioner, in search for a simplified and intuitive understanding of the effects of nonlinearities on the dynamic response of cable structures (to confirm and explain results from more detailed FEM models), the proposed approach also paves the way for the investigation in the extensive taxonomy of the non-linear dynamic behaviour of cable structures. The present paper focuses on non-linear normal modes (NNMs) arising as a continuation of linear vibration modes of the structure when energy is increased. The identification of non-linear normal modes is achieved through harmonic balance; a time-integration analysis is then performed on the same model, with initial conditions derived from the harmonic balance approach, demonstrating consistent results. To further test the model, its behaviour is compared to simulations on a 66-degrees of freedom finite element truss model, with satisfactory results.

介绍了预应力索桁架的非线性动态行为模型。该模型为简化描述双凹和双凸索结构（以及单索）在不同载荷（和质量分布）条件下的（平面内）非线性动力学行为提供了基础。所提出方法的简单性与其在不同垂直载荷条件下示意性表示各种实际结构的能力相结合，包括轻型行人悬索桥和带有垂直线束的电缆屋顶。虽然针对从业者的需求，寻求对非线性对索结构动力响应影响的简化和直观理解（以确认和解释更详细的 FEM 模型的结果），所提出的方法还为电缆结构非线性动态行为的广泛分类研究铺平了道路。本论文侧重于当能量增加时作为结构线性振动模式的延续而出现的非线性正常模式 (NNM)。通过谐波平衡实现非线性常模的识别；然后对同一模型进行时间积分分析，初始条件源自谐波平衡方法，证明结果一致。为了进一步测试模型，将其行为与 66 自由度有限元桁架模型的模拟进行比较，结果令人满意。本论文侧重于当能量增加时作为结构线性振动模式的延续而出现的非线性正常模式 (NNM)。通过谐波平衡实现非线性常模的识别；然后对同一模型进行时间积分分析，初始条件源自谐波平衡方法，证明结果一致。为了进一步测试模型，将其行为与 66 自由度有限元桁架模型的模拟进行比较，结果令人满意。本论文侧重于当能量增加时作为结构线性振动模式的延续而出现的非线性正常模式 (NNM)。通过谐波平衡实现非线性常模的识别；然后对同一模型进行时间积分分析，初始条件源自谐波平衡方法，证明结果一致。为了进一步测试模型，将其行为与 66 自由度有限元桁架模型的模拟进行比较，结果令人满意。初始条件源自谐波平衡方法，显示出一致的结果。为了进一步测试模型，将其行为与 66 自由度有限元桁架模型的模拟进行比较，结果令人满意。初始条件源自谐波平衡方法，显示出一致的结果。为了进一步测试模型，将其行为与 66 自由度有限元桁架模型的模拟进行比较，结果令人满意。