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首页> 外文期刊>International journal of bifurcation and chaos in applied sciences and engineering >Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks
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Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks

机译：普通和细长刚性块的非线性摆动动力学中的异斜度分叉和最优控制

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摘要

A method for controlling nonlinear dynamics and chaos, previously developed by the authors, is applied to the rigid block on a moving foundation. The method consists in modifying the shape of the excitation in order to eliminate, in an optimal way, the heteroclinic intersections embedded in the system dynamics. Two different cases are examined: (i) generic block under small perturbations and (ii) slender block under generic perturbations, and they are investigated analytically either by a perturbation analysis (former case) or exactly (latter case). Two different strategies are proposed: (i) one-side control, which consists in eliminating the intersections of a single heteroclinic connection, and (ii) global control, which consists in simultaneously eliminating the intersections of both heteroclinic connections. The best excitations permitting the maximum distance between stable and unstable manifolds are determined in both cases. Finally, some numerical investigations aimed at highlighting meaningful aspects of system response under controlled (optimal) and noncontrolled (harmonic) excitations are performed.
机译：作者先前开发的一种控制非线性动力学和混沌的方法被应用于运动基础上的刚性砌块。该方法包括修改激励的形状，以便以最佳方式消除嵌入系统动力学中的异质交叉。研究了两种不同的情况：（i）小扰动下的通用块，（ii）普通扰动下的细长块，并通过扰动分析（前一种情况）或精确地（后一种情况）进行了分析研究。提出了两种不同的策略：（i）单侧控制，其包括消除单个异质连接的交点，以及（ii）全局控制，其包括同时消除两个异斜连接的交点。在这两种情况下，都应确定允许在稳定歧管和不稳定歧管之间的最大距离的最佳激励。最后，进行了一些数值研究，旨在突出在受控（最佳）和非受控（谐波）激励下系统响应的有意义的方面。

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