Dynamical response of a rocking rigid block.
Dynamical response of a rocking rigid block.
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DOI：
10.1063/5.0040962
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发表时间：
2021-07
期刊：
影响因子：
2.9
通讯作者：
Y. Liu;J. Páez Chávez;P. Brzeski;P. Perlikowski
中科院分区：
文献类型：
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作者：
Y. Liu;J. Páez Chávez;P. Brzeski;P. Perlikowski
本文研究了刚性块体结构在谐波地面激励下的复杂动力行为，从而模拟了系统在地震激励下或船舶上的集装箱在海浪周期性作用下的振动。推导了运动方程，假设在块体和地面之间的界面处有很大的摩擦系数，这样就不会发生滑动。此外，数学模型假定在与地面发生碰撞时动能会损失。然后在脉冲动力系统的框架下建立和研究了得到的数学模型。使用两种不同的方法详细研究了其复杂的动态响应，基于直接数值积分和路径跟踪技术，其中路径跟踪通过延续平台COCO实现（Dankowicz和Schilder）。我们的研究揭示了各种动力学现象的存在，如分支点、极限环的折叠和倍周期分岔、对称和非对称周期响应以及混沌运动。利用盆稳定性方法，我们还研究了解的性质及其在相空间和参数空间中的存在范围。此外，该研究还考虑了导致块体结构倾覆的地面激励条件，并给出了可以避免这种行为的参数区域。
This paper investigates the complex dynamical behavior of a rigid block structure under harmonic ground excitation, thereby mimicking, for instance, the oscillation of the system under seismic excitation or containers placed on a ship under periodic acting of sea waves. The equations of motion are derived, assuming a large frictional coefficient at the interface between the block and the ground, in such a way that sliding cannot occur. In addition, the mathematical model assumes a loss of kinetic energy when an impact with the ground takes place. The resulting mathematical model is then formulated and studied in the framework of impulsive dynamical systems. Its complex dynamical response is studied in detail using two different approaches, based on direct numerical integration and path-following techniques, where the latter is implemented via the continuation platform COCO (Dankowicz and Schilder). Our study reveals the presence of various dynamical phenomena, such as branching points, fold and period-doubling bifurcation of limit cycles, symmetric and asymmetric periodic responses, and chaotic motions. By using the basin stability method, we also investigate the properties of solutions and their ranges of existence in phase and parameter spaces. Moreover, the study considers ground excitation conditions leading to the overturning of the block structure and shows parameter regions wherein such behavior can be avoided.