Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis
From MaRDI portal
Publication:1249548
DOI10.1016/0005-1098(78)90036-5zbMath0385.93028OpenAlexW1984578963MaRDI QIDQ1249548
Jerrold E. Marsden, Philip J. Holmes
Publication date: 1978
Published in: Automatica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0005-1098(78)90036-5
Control/observation systems governed by partial differential equations (93C20) Nonlinear systems in control theory (93C10) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Bifurcations in context of PDEs (35B32) Local and nonlocal bifurcation theory for dynamical systems (37G99)
Related Items
Energy convergence results for strongly damped nonlinear wave equations, A double Hopf bifurcation phenomenon, Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances, A STRANGE ATTRACTOR WITH LARGE ENTROPY IN THE UNFOLDING OF A LOW RESONANT DEGENERATE HOMOCLINIC ORBIT, The codimension-two bifurcation for the recent proposed SD oscillator, Analysis of limit cycle oscillations of a typical airfoil section with freeplay, Asymptotic finite-dimensional approximations for a class of extensible elastic systems, Liapunov stability properties in second order evolution equations with finite memory, Elastic stabilization of an intrinsically unstable hyperbolic flow–structure interaction on the 3D half-space, Elastic membrane equation with dynamic boundary conditions and infinite memory, On one mathematical model in elastic stability theory, Nonlinear resonant responses, mode interactions, and multitime periodic and chaotic oscillations of a cantilevered pipe conveying pulsating fluid under external harmonic force, On the analysis of Hopf bifurcations, Parametric oscillations of nonlinear flutter systems, Flow-plate interactions: well-posedness and long-time behavior, Controllability near Takens-Bogdanov points, Long—time behaviour of strong solutions of retarded nonlinear P.D.E.s, A rotating disk linked by a pair of springs, Unnamed Item, Properties of Center Manifolds, Symplectic analysis of dynamical systems with a small parameter. A new criterion for stabilization of homoclinic separatrices and its application, Stability properties of non-constant stationary solutions of the periodic korteweg-de vries Equation, Limiting behavior of strongly damped nonlinear wave equations, A cubic Hénon-like map in the unfolding of degenerate homoclinic orbit with resonance, The convergence of a Galerkin approximation scheme for an extensible beam, Chaos in mechanical systems -- a review, Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions, Feedback Stabilization of a Fluttering Panel in an Inviscid Subsonic Potential Flow, A thorough look at the (in)stability of piston-theoretic beams, Convergence of singular perturbations of strongly damped nonlinear wave equations, Stability analysis of a rotating flexible system, Bifurcation of periodics and subharmonics in abstract nonlinear undamped wave equations, A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam, ESTIMATION OF CHAOTIC THRESHOLDS FOR THE RECENTLY PROPOSED ROTATING PENDULUM, Long-time dynamics of Balakrishnan-Taylor extensible beams, Large deflections of inextensible cantilevers: modeling, theory, and simulation, Dissipative operators with finite dimensional damping, The application of centre manifolds to amplitude expansions. I. Ordinary differential equations, Bifurcation and stability analysis of static equilibrium configuration of curved pipe conveying fluid, Nonlinear second order equations with applications to partial differential equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bifurcation formulae derived from center manifold theory
- The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
- Decay to zero in critical cases of second order ordinary differential equations of Duffing type
- Bifurcations and trajectories joining critical points
- Generic one-parameter families of vector fields on two-dimensional manifolds
- Singularities of vector fields
- The stable, center-stable, center, center-unstable, unstable manifolds
- Non-linear semi-groups
- Stability theory for an extensible beam
- Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis
- Differentiable dynamical systems
- LECTURES ON BIFURCATIONS IN VERSAL FAMILIES
- Invariant manifolds