Stabilization of the generalized Rao‐Nakra beam by partial viscous damping

Abstract

In this paper, we consider the stabilization of the generalized Rao-Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angle of the top and bottom layers and one Euler-Bernoulli beam equation for the transversal displacement. Dissipative mechanism are provided through viscous damping for two displacements. The location of the viscous damping are divided into two groups, characterized by whether both of the top and bottom layers are directly damped or otherwise. Each group consists of three cases. We obtain the necessary and sufficient conditions for the cases in group 2 to be strongly stable. Furthermore, polynomial stability of certain orders are proved. The cases in group 1 are left for future study.

Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type

“…Mukiawa [16] recently studied system (1) with linear damping and Gurtin-Pipkin's thermal law for heat conduction, proving the existence and establishing an exponential decay rate. Additional results on multilayer beams can be found in [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Asymptotic behavior of the Rao–Nakra sandwich beam model with Kelvin–Voigt damping

“…Moreover, if two of the three equations are damped, only polynomial stability is possible [19, 20]. But, if internal viscous damping acts on only one of the three Rao–Nakra beam equations, then polynomial decay rate is sensitive to various boundary conditions and damping locations [21].…”