The purpose of this manuscript is to establish well posedness as well as the existence of global and exponential attractor for a nonlinear Timoshenko system subject to control terms in the two equations of the system. Since the control terms act on both equations, we will not use the nonphysical relationship known as equal speeds of propagation of waves. A combination involving friction-delay and friction controls will act on the angle of rotation equation, while a nonlinear friction control will act on the transverse motion equation. The result will be established by showing that the system is quasi-stable and by using a relationship involving the size of the friction type controls inserted in the rotation angle equation.

中文翻译：

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具有离散延迟项和非线性阻尼的非线性 Timoshenko 梁的长期动力学

这篇手稿的目的是为非线性 Timoshenko 系统建立适定性以及全局和指数吸引子的存在，该系统受系统的两个方程中的控制项约束。由于控制项作用于两个方程，因此我们不会使用称为等速波传播的非物理关系。涉及摩擦延迟和摩擦控制的组合将作用于旋转角度方程，而非线性摩擦控制将作用于横向运动方程。结果将通过显示系统是准稳定的，并通过使用涉及插入旋转角方程的摩擦类型控件的大小的关系来建立。