Nonlinear oscillations of a fluttering plate resting on a unidirectional elastic foundation
A single, simply supported plate resting on a unidirectional elastic foundation was studied for nonlinear oscillation. Linear quasi-steady supersonic theory (piston theory) is used for the aerodynamic pressure. The aeroelastic equations of motion are derived using a hybrid Rayleigh-Ritz-Galerkin method, and a vectorized numerical scheme is developed for efficient time integration in the MATLAB environment. It is shown that the flutter boundary of a plate resting on a unidirectional elastic foundation is approximately independent of compressive foundation stiffness and nearly identical to that of a plate alone. The limit cycle behavior is, however, strongly dependent on the compressive foundation stiffness and tends to favor chaotic oscillations about a mean position significantly above the nominal foundation position, especially at higher foundation stiffness values. The flutter boundary predictions of linear theory tend to break down in this very high foundation stiffness regime as well.
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