Instability of modes in a partially hinged rectangular plate

DOI10.1016/j.jde.2016.08.037zbMath1361.35025arXiv1608.07082OpenAlexW2963018773MaRDI QIDQ324113

Vanderley jun. Ferreira, Ederson Moreira dos Santos, Gazzola, Filippo

Publication date: 10 October 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.07082

zbMATH Keywords

well-posednessnonlocal plate equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Plates (74K20) Stability of solutions to ordinary differential equations (34D20) Initial-boundary value problems for higher-order hyperbolic equations (35L35) PDEs in connection with mechanics of deformable solids (35Q74) Higher-order semilinear hyperbolic equations (35L76)

Related Items (17)

Stability of a suspension bridge with a localized structural damping ⋮ Stabilization of a suspension bridge with locally distributed damping ⋮ Asymptotic finite-dimensional approximations for a class of extensible elastic systems ⋮ Numerical solution to the linearized model of a clamped-free plate using nonconforming finite elements ⋮ Resonance tongues for the Hill equation with Duffing coefficients and instabilities in a nonlinear beam equation ⋮ A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges ⋮ Long-time dynamics of a hinged-free plate driven by a nonconservative force ⋮ Steady Navier-Stokes equations in planar domains with obstacle and explicit bounds for unique solvability ⋮ Existence and stability results of a plate equation with nonlinear damping and source term ⋮ Stability of a suspension bridge with structural damping ⋮ An evolution von Kármán equation modeling suspension bridges ⋮ Long-time behavior of partially damped systems modeling degenerate plates with piers ⋮ Eight(y) mathematical questions on fluids and structures ⋮ Stability analysis in some strongly prestressed rectangular plates ⋮ Uniform decay rates for a suspension bridge with locally distributed nonlinear damping ⋮ Periodic Solutions and Torsional Instability in a Nonlinear Nonlocal Plate Equation ⋮ Convergence analysis of virtual element method for nonlinear nonlocal dynamic plate equation

Uses Software

• SciPy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A partially hinged rectangular plate as a model for suspension bridges
• Nonlinear questions in clamped plate models
• On the justification of plate models
• Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions
• Nonlinear buckled states of rectangular plates
• Hinged and supported plates with corners
• Mathematical models for suspension bridges. Nonlinear structural instability
• A clamped plate with a uniform weight may change sign
• In any dimension a ``clamped plate with a uniform weight may change sign
• Bending and stretching energies in a rectangular plate modeling suspension bridges
• Initial-boundary value problems for an extensible beam
• Stability of simple modes of the Kirchhoff equation
• ENERGY RELATIONS FOR A SUSPENDED CABLE
• The Bending and Stretching of Plates
• Real Interpolation of Sobolev Spaces on Subdomains of Rn
• The Stability of the Equilibrium of a Nonlinear Hill’s Equation
• Unstable simple modes of the nonlinear string
• Modeling suspension bridges through the von Kármán quasilinear plate equations

This page was built for publication: Instability of modes in a partially hinged rectangular plate