Boundary Feedback Stabilization for the Intrinsic Geometrically Exact Beam Model

DOI10.1137/20M1340010zbMath1458.35260arXiv1912.02543OpenAlexW2993242732MaRDI QIDQ5139668

Charlotte Rodriguez, Günter R. Leugering

Publication date: 10 December 2020

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02543

zbMATH Keywords

exponential stabilizationboundary feedbackgeometrically exact beamintrinsic beamone-dimensional first-order semilinear hyperbolic systems

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stabilization of systems by feedback (93D15) Initial-boundary value problems for first-order hyperbolic systems (35L50)

Related Items (3)

Networks of geometrically exact beams: well-posedness and stabilization ⋮ Nodal profile control for networks of geometrically exact beams ⋮ Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability and boundary stabilization of 1-D hyperbolic systems
• Large time asymptotics for partially dissipative hyperbolic systems
• Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems
• A finite strain beam formulation. The three-dimensional dynamic problem. I
• On finite deformations of space-curved beams
• Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms
• Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control
• A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams
• Exact controllability for nonautonomous first order quasilinear hyperbolic systems
• Stabilization of Bernoulli--Euler Beams by Means of a Pointwise Feedback Force
• Classical Solutions of Nonlinear Beam Equations: Existence and Stabilization
• Boundary Control of the Timoshenko Beam
• Boundary control of a Timoshenko beam attached to a rigid body: planar motion
• Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping
• Modelling of dynamic networks of thin thermoelastic beams
• Networks of Nonlinear Thin Structures - Theory and Applications
• Boundary Feedback Stabilization of the Undamped Euler--Bernoulli Beam with Both Ends Free
• Boundary feedback exponential stabilization of a Timoshenko beam with both ends free
• Control of Planar Networks of Timoshenko Beams
• Dynamic Domain Decomposition of Optimal Control Problems for Networks of Strings and Timoshenko Beams
• Arbitrary Decay Rate for Euler-Bernoulli Beam by Backstepping Boundary Feedback
• Exponential Stability of Semi-linear One-Dimensional Balance Laws
• Simulation and structural optimization of 3d Timoshenko beam networks based on fully analytic network solutions

This page was built for publication: Boundary Feedback Stabilization for the Intrinsic Geometrically Exact Beam Model