In this paper, we consider a one-dimensional laminated beam with structural damping and an infinite memory acting on the effective rotation angle. Under appropriate assumptions imposed on the relaxation function, we show that the system is well-posed by using the Hille–Yosida theorem, and then we establish general decay results, from which exponential and polynomial decays are only special cases, in the case of equal speeds of wave propagation as well as that of nonequal speeds. In the particular case when the wave propagation speeds are different and the relaxation function decays exponentially, we show the lack of exponential stability.

中文翻译：

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具有结构阻尼和无限记忆的层合梁的渐近稳定性

在本文中，我们考虑具有结构阻尼和作用于有效旋转角的无限记忆的一维层压梁。在对松弛函数施加适当的假设下，我们通过使用 Hille-Yosida 定理证明系统是适定的，然后我们建立了一般衰减结果，其中指数和多项式衰减只是特殊情况，在相等的情况下波传播的速度以及不等速的传播速度。在波传播速度不同且弛豫函数呈指数衰减的特殊情况下，我们表现出缺乏指数稳定性。