Nonlinear Dynamics of Solids, Shells, and Rods

10:00 AM-12:30 PM

*Room: White Pine*

The speakers in this minisymposium will address theoretical and computational aspects of nonlinear dynamics of solids especially structures such as shells and rods used by engineers. Energy-momentum and dissipative integration schemes, reduction methods, existence of inertial manifolds, chaotic and regular motion in shells are some aspects of the minisymposium: (1) Since the stability property of time integration schemes become very important when dealing with very large systems, robust integration schemes have to be constructed. Efforts recently taken in developing mechanical integrators that preserve the essential features of the mechanical system, e.g., the momemtum, the energy, or the symplectic structure, will be focused on. (2) Several ideas of extending some techniques and applications of reduction methods, that were originally developed in the context of Fluid Mechanics, to the context of the Theory of Elasticity and Solid Structures will be given. Applications to mechanical structures of the POD method, the nonlinear Galerkin or the post processed Galerkin method to approximate Inertial Manifolds, will be discussed. (3) Birfurcations, chaotic and free large over-all motion of such structures are of interest and will be taken as examples.

**Organizers: Peter Wriggers and Carlo Sansour**

*Darmstadt University of Technology, Germany*

**10:00-10:25 Postprocessing Galerkin Methods**- Edriss Titi, University of California, Irvine
**10:30-10:55 Nonlinear Oscillations of a Fluid Conveying Tube with an End Mass***Alois Steindl*, Hans Troger, and Bernhard Albrecht, Vienna University of Technology, Austria**11:00-11:25 Time-Stepping Algorithms with Controllable High-Frequency Dissipation for Nonlinear Dynamics***Francisco Armero*and Ignacio Romero, University of California, Berkeley**11:30-11:55 The Post-Processed Galerkin Method Applied to Nonlinear Shell Vibrations***Carlo R. Laing*, University of Pittsburgh; and Allan McRobie, Cambridge University, United Kingdom**12:00-12:25 Geometric Exact Models, Energy-Momentum Methods, and Active Degrees of Freedom for the Dynamics of Shells and Rods**

*Carlo Sansour*and Petter Wriggers, Organizers; and Jamal Sansour, University of Hannover, Germany

*MMD, 3/18/99*