A piezoelectric Euler-Bernoulli beam with dynamic boundary control: stability and dissipative FEM

DOI10.1007/s10440-014-9965-1zbMath1326.35034arXiv1507.02542OpenAlexW2027118517MaRDI QIDQ2355759

Maja Miletić, Anton Arnold

Publication date: 28 July 2015

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.02542

zbMATH Keywords

error estimatesboundary feedback controlclosed-loop control systemdissipative Galerkin method

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stabilization of systems by feedback (93D15) Stability in context of PDEs (35B35) Finite element methods applied to problems in solid mechanics (74S05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (6)

Exponential decay rate of a nonlinear suspension bridge model by a local distributed and boundary dampings ⋮ Exponential stability and numerical treatment for piezoelectric beams with magnetic effect ⋮ Unnamed Item ⋮ A Numerical Study for a Flexible Euler-Bernoulli Beam with a Force Control in Velocity and a Moment Control in Rotating Velocity ⋮ Riesz basis and exponential stability of a variable coefficients rotating disk-beam-mass system ⋮ An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An Euler-Bernoulli-like finite element method for Timoshenko beams
• Optimal energy decay for a nonhomogeneous flexible beam with a tip mass
• Stabilization of a hybrid system of elasticity by feedback boundary damping
• Infinite-dimensional dynamical systems in mechanics and physics
• Stability and stabilization of infinite dimensional systems with applications
• Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam
• On the boundary control of a hybrid system with variable coefficients
• Entropy decay of discretized Fokker-Planck equations. I: Temporal semidiscretization
• Hamiltonian discretization of boundary control systems
• Feedback control of flexible systems
• Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients
• Stabilization and disturbance rejection for the beam equation
• Uniform Stabilization of a Hybrid System of Elasticity
• Exponential Stability of a Class of Boundary Control Systems
• The Mathematical Theory of Finite Element Methods
• Riesz Basis Generation of Abstract Second-Order Partial Differential Equation Systems with General Non-Separated Boundary Conditions
• Lyapunov-Based Vibration Control of Translational Euler-Bernoulli Beams Using the Stabilizing Effect of Beam Damping Mechanisms
• Numerical schemes for the estimation of functional parameters is distributed models for mixing mechanisms in lake and sea sediment cores

This page was built for publication: A piezoelectric Euler-Bernoulli beam with dynamic boundary control: stability and dissipative FEM