The Fluttering Panel as a Continuous Nonlinear Nonconservative System

Abstract

A nonlinear continuous elastic system subjected to a combination of conservative and nonconserv ative forces is considered where parameters controlling the system are moving deep in the instability domain. New techniques are employed to present the numerical results in a compact form suitable for the interpreta tion of the system postcritical behavior. As an example, an initially planar elastic rectangular panel subjected to supersonic gas flow and loaded in the middle surface by "dead" forces is considered. Classical plate theory and piston theory approximation are used to simplify the statement and analysis of the problem. The steady states of the systems and their stability are analyzed without discretization of the problem, that is, within the framework of continuum solid mechanics. When dynamic behavior is concerned, the study is performed for a finite-degree-of-freedom approximation of the system. However, the number of degrees of freedom is cho sen to be high enough to address the main features of the continuous system, and the final numerical results are discussed in terms of continuum systems. A variety of attractors is found in remote postcritical domains, and the high sensitivity of the system behavior to the variation of the control parameters and initial conditions is demonstrated.