Stabilization results for well-posed potential formulations of a current-controlled piezoelectric beam and their approximations

DOI10.1007/s00245-020-09665-4zbMath1475.78003OpenAlexW3011636035MaRDI QIDQ2045142

Ahmet Özkan Özer

Publication date: 11 August 2021

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-020-09665-4

zbMATH Keywords

stabilizationMaxwell's equationsdistributed parameter systemCoulomb gaugeelectromagnetic potentialsLorenz gaugefully dynamiccurrent-controlled piezoelectric beams

Mathematics Subject Classification ID

Feedback control (93B52) Electromagnetic effects in solid mechanics (74F15) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Finite difference methods applied to problems in solid mechanics (74S20) Technical applications of optics and electromagnetic theory (78A55) Electromagnetic theory (general) (78A25) Problems involving hysteresis in solids (74N30)

Related Items (5)

Longtime dynamics for a novel piezoelectric beam model with creep and thermo-viscoelastic effects ⋮ Stabilization of nonlinear non-uniform piezoelectric beam with time-varying delay in distributed control input ⋮ Existence and robustness results of attractors for partially-damped piezoelectric beams ⋮ Stabilization results of a piezoelectric beams with partial viscous dampings and under Lorenz gauge condition ⋮ Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform stabilization of a multilayer Rao-Nakra sandwich beam
• Further stabilization and exact observability results for voltage-actuated piezoelectric beams with magnetic effects
• Stabilization and shape control of a 1D piezoelectric Timoshenko beam
• Uniform boundary stabilization of the finite difference space discretization of the 1-D wave equation
• Semigroups of linear operators and applications to partial differential equations
• Rational energy decay rate for a wave equation with dynamical control
• Local well-posedness of the \((4 + 1)\)-dimensional Maxwell-Klein-Gordon equation at energy regularity
• Piezoelectric shells. Sensing, energy harvesting, and distributed control
• A general framework for the study of indirect damping mechanisms in elastic systems
• Piezoelectromagnetic waves in a ceramic plate between two ceramic half-spaces
• Long-time dynamics for a fractional piezoelectric system with magnetic effects and Fourier's law
• Modeling and Stabilizability of Voltage-Actuated Piezoelectric Beams with Magnetic Effects
• Finite-Energy Global Well-Posedness of the Maxwell–Klein–Gordon System in Lorenz Gauge
• Modeling and Controlling an Active Constrained Layer (ACL) Beam Actuated by Two Voltage Sources With/Without Magnetic Effects
• Exponential stability and numerical treatment for piezoelectric beams with magnetic effect
• Potential Formulation for Charge or Current-Controlled Piezoelectric Smart Composites and Stabilization Results: Electrostatic Versus Quasi-Static Versus Fully-Dynamic Approaches
• Smart Material Systems
• Precision position control of piezoelectric actuators using charge feedback
• Modeling and stabilization of current-controlled piezo-electric beams with dynamic electromagnetic field
• Spectral analysis of a non-selfadjoint operator generated by an energy harvesting model and application to an exact controllability problem
• Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation
• Exact Boundary Controllability Results for a Multilayer Rao--Nakra Sandwich Beam
• Construction of the Theory of Piezoelectric Shells and Plates

This page was built for publication: Stabilization results for well-posed potential formulations of a current-controlled piezoelectric beam and their approximations