Nonlinear theoretical aeroelastic model of a plate: Free to fixed in-plane boundaries

It is well known that the nonlinear response of a beam or plate is sensitive to the assumptions made about the in-plane boundary constraints. This is true for any static or dynamic loading, and especially for aerodynamic loads that may lead to a dynamic instability and limit cycle oscillations. In the present paper, a mathematical and computational model for the general case has been created to allow for the full range of in-plane boundary constraints to be considered. This is of fundamental interest but is also of considerable practical interest, in that physical structures usually fall somewhere between the two limiting cases. Moreover, it is shown that prior models of even the limiting cases are, at best, approximations of these special cases; and comparisons between the present model and prior models provide new insights into these issues. The model is also correlated with a recent hypersonic wind-tunnel experiment. The effect of in-plane constraints is investigated on buckling, vibration about a nonlinear deformed state due to static pressure differential, flutter onset, and postflutter limit cycle oscillation.