Papers Published

1. Smelova, Tatyana V. and Dowell, Earl H., On necessary conditions for chaotic motion of a buckled plate with external excitation in an aerodynamic flow, American Society of Mechanical Engineers, Applied Mechanics Division, AMD, vol. 192 (1994), pp. 327 - 332 .
   (last updated on 2007/04/10)

   Abstract:
   We study the system of the modal Galerkin equations of motion of a buckled plate with external exitation in an aerodynamic flow using the famous Melnikov method. The possibility of the occurrence of chaos is considered through the behavior of the stable and unstable manifolds of the unstable unperturbed equilibrium. The condition for the intersection of the manifolds is a necessary condition for the complex motion of tile system. The Melnikov algorithm is applied to a multiple degree-of-freedom system. The second and higher modes are not assumed to be small. It is established that the influence of the second mode cannot be neglected. The suggested form of the critical relation between the system parameters is a generalization of the well known Holmes result for the single degree-of-freedom case. The one-dimensional and multi-dimensional relations differ by the calculated function of the axial load and the number of modes.

   Keywords:
   Plates (structural components);Flutter (aerodynamics);Aerodynamic loads;Buckling;Algorithms;Chaos theory;System stability;Equations of motion;Mathematical models;Perturbation techniques;Degrees of freedom (mechanics);