Liu, Wenjun; Kong, Xiangyu; Li, Gang Asymptotic stability for a laminated beam with structural damping and infinite memory. (English) Zbl 07259267 Math. Mech. Solids 25, No. 10, 1979-2004 (2020). Summary: 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. Cited in 14 Documents MSC: 74-XX Mechanics of deformable solids Keywords:general stability; infinite memory; multiplier technique; energy method PDFBibTeX XMLCite \textit{W. Liu} et al., Math. Mech. Solids 25, No. 10, 1979--2004 (2020; Zbl 07259267) Full Text: DOI References: [1] Hansen, SW . A model for a two-layered plate with interfacial slip. In: Desch, W, Kappel, F, Kunisch, K (eds) Control and estimation of distributed parameter systems: nonlinear phenomena (International Series of Numerical Mathematics, vol. 118). Basel: Birkhäuser, 1994, 143-170. · Zbl 0810.73026 [2] Hansen, SW, Spies, R. Structural damping in a laminated beams due to interfacial slip. J Sound Vib 1997; 204(2): 183-202. [3] Wang, JM, Xu, GQ, Yung, SP. Exponential stabilization of laminated beams with structural damping and boundary feedback controls. SIAM J Control Optim 2005; 44(5): 1575-1597. · Zbl 1132.93021 [4] Cao, XG, Liu, DY, Xu, GQ. 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