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Analysing Vibrations of Dissipative Structures with Connection Disruption

机译：用连接破坏分析耗散结构的振动

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The article contains the mathematical models of vibrations and the algorithm to calculate a constructive nonlinear system in case of a sudden failure process in a connection. The calculation model of the structure is viewed as a discreet dissipative system. From the position of time analysis, the author derives the governing equation of the system reaction under static load before the failure. The author has conducted the analysis of the system reaction and has proved certain dependence for its parameters at the moment of connection fracture. For the critical time point we obtained the kinematic (movements, velocities and accelerations) and force parameters of reaction (restoring, dissipative and inertial forces) in two states of the calculation model: before and after the fracture. The article contains the derivation of analytical expressions defining the leap size of the dynamic reaction parameters of the calculation model at the moment of its damage. The author has presented the auxiliary reaction which allows one to evaluate the side effect caused by the constructive element disruption. The side effect reaction equation presents a vector difference of the reaction after and before the damage. The results are illustrated by the example of a two span steel beam the vibrations of which were caused by the sudden destruction of an intermediate support. The evaluation of the solution accuracy is also presented.
机译：该文章包含振动的数学模型和算法，用于在连接中突然发生故障过程的情况下计算建设性非线性系统。将结构的计算模型视为谨慎的耗散系统。从时间分析的位置，作者在故障前静态负载下导出系统反应的控制方程。作者对系统反应进行了分析，并在连接骨折时证明了其参数的某些依赖。对于临界时间点，我们在计算模型的两个状态下获得了运动（运动，速度和加速度）和力的反应（恢复，耗散和惯性力）的力参数：在骨折之前和之后。本文包含在损坏时定义计算模型动态反应参数的飞跃大小的分析表达式的推导。作者提出了辅助反应，其允许人们评估由建设性元素破坏引起的副作用。副作用反应方程呈现在损伤之后和之前反应的载体差异。结果通过两个跨度钢束的示例说明了由突然破坏中间支撑件引起的振动。还提出了对溶液精度的评估。

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