Exponential stability of the semigroup associated with a non-homogeneous flexible beam with boundary damping. (English) Zbl 1163.35432
Summary: We show the exponential stability of the semigroup associated with the Euler-Bernoulli beam equation with boundary damping at one end, where the bending moment and shear force applied to that end are given in feedback form. In the model, we consider a non-homogeneous beam wherein the density, stiffness and damping depend on the spatial variable \(x\).
MSC:
35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
35L75 | Higher-order nonlinear hyperbolic equations |
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
35B35 | Stability in context of PDEs |
35B40 | Asymptotic behavior of solutions to PDEs |
93D15 | Stabilization of systems by feedback |