Abstract—

We study the stability of a one-dimensional laminated beam which consists of two identical layers of uniform thickness. An adhesive of small thickness is bonding the two layers and creating a restoring force thereby producing a damping called adhesive or structural damping at the interface. It is well-known in the literature that this single frictional damping is not strong enough to stabilize the system exponentially. On the contrary, we prove in this paper that the unique dissipation due to the structural damping is strong enough to exponentially stabilize the system provided the wave speeds of the system are equal.

中文翻译：

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界面滑移的层合梁的指数稳定性

摘要-

我们研究一维层合梁的稳定性，该层合梁由两个相同且厚度相同的相同层组成。小厚度的粘合剂将两层粘合在一起并产生恢复力，从而在界面处产生称为粘合剂的阻尼或结构阻尼。在文献中众所周知，这种单一的摩擦阻尼不足以使系统成指数地稳定。相反，我们在本文中证明，只要系统的波速相等，由于结构阻尼而产生的独特耗散足以使系统指数级地稳定。