Nonlinear LCO “amplitude–frequency” characteristics for plates fluttering at supersonic speeds

• Due to the aerodynamic quadratic nonlinearity the character of the "amplitude-frequency" characteristics of the plate in a supersonic gas flow can be identical to the character of this dependence in the case of non-linear oscillations of shells.
• Undamped nonlinear oscillations may occur in the case of both pre- and post- critical speeds. Transition from one type of "amplitude-frequency" dependency to another can be achieved not only with an appropriate choice of the geometrical parameters of the aeroelastic system, but also by changing the value of the flow speed.
• For relatively thick plates, in a post- critical state, there exists a range of frequency, out of which no stable LCOs are obtained. Moreover, in a critical state flutter can be excited at low frequencies.

The nonlinear aeroelastic behavior of isotropic rectangular plates in supersonic gas flow is examined. Quadratic and cubic aerodynamic nonlinearities as well as cubic geometrical nonlinearities are considered in this study. While the aerodynamic nonlinearities are the results of the expansion of the nonlinear piston-theory aerodynamics loading up to the third-order, the geometrical nonlinearities are due to stiffening effects from the panel out-of-plane deformation consistent with the von Karman’s nonlinear plate theory. While in vacuum the typical nonlinear hardening frequency vs. oscillation amplitude, one characterized by monotonically increasing amplitudes at increasing frequencies, exists, in the presence of a high-speed flow, qualitative and quantitative changes of the nonlinear relationship are expected. This paper shows how the thin-plate behavior is influenced by the high-speed flows providing the “amplitude–frequency” dependency, which describes the nonlinear oscillations of the considered aeroelastic system.