Exponential stabilization of a structure with interfacial slip

Abstract

Two exponential stabilization results are proved for a vibrating structure subject to an interfacial slip. More precisely, the structure consists of two identical beams of Timoshenko type and clamped together but allowing for a longitudinal movement between the layers. We will stabilize the system through a transverse friction and also through a viscoelastic damping.2010 Mathematics Subject Classification. 34B05, 34D05, 34H05.

Well‐posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks

“…For stability of laminated Timoshenko beams with structural memory, one can refer to the previous studies. [23][24][25][26] For laminated Timoshenko beams with second sound, one can find a stability result in Apalara. 27 The delay effects often appears in many practical problems, for instance, chemical, physical, thermal, and economic phenomena, and may turn a well-behaved system into a wild one.…”

Stability of a thermoelastic laminated system subject to a neutral delay

“…Summing up the identities (37) and (38) and estimating the different remaining terms, we obtain (36).…”

“…Lo) in a series of papers. [34][35][36][37] Recently, the well-posedness and the exponential stability of a thermoelastic laminated beam with Gurtin-Pipkin thermal law have been studied in Liu and Zhao. 38 The studied problem was…”

On a Thermoelastic Laminated Timoshenko Beam: Well Posedness and Stability

“…By adding suitable damping effects, such as internal damping, (boundary) frictional damping, and viscoelastic damping, it was shown that if the linear damping terms are added in two of the three equations, system (4) is exponentially stable under the "equal wave speeds" assumption (ρ/I ρ ) � (G/D). But if the damping terms are added in the three equations, then the system decays exponentially without the equal wave speeds assumption, see, for example, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For thermoelastic laminated Timoshenko beam, there are few published works, we can mention the results due to Liu and Zhao [18] and Apalara [19].…”