Nonlinear plate aeroelastic response with uncertain stiffness and boundary conditions

Abstract

The probabilistic response of a nonlinear panel in supersonic flow is investigated using a new computational methodology. The aeroelastic system is modelled by coupling the von Karman plate equations with piston theory aerodynamics. Baseline deterministic results are compared to published data to establish validity of the aeroelastic model. Uncertainties in modulus of elasticity and boundary conditions (BCs) are considered, with their impact on panel response being quantified in terms of limit-cycle oscillation (LCO) onset pressure and panel amplitude. The panel's uncertain BCs are modelled using rotational springs in place of ideally fixed boundary conditions. The panel's uncertain elastic modulus is modelled as a second-order, spatially homogeneous, isotropic, random field. The boundary spring stiffness values are spatially constant for each random realization assuming either a uniform or Weibull distribution. Probabilistic response distributions are obtained through Monte Carlo simulation (MCS) for selected values of flowfield dynamic pressure. MCS is run for the case of random modulus only, as well as random modulus combined with either random BC distribution. It is observed that uncertainties have the greatest nonlinear influence on LCO amplitude near the deterministic point of LCO onset. Furthermore, panel response is much more sensitive to location of the modulus fields' extreme values than the correlation length used to generate the field. Novel aspects of the computational methodology include (1) the use of random fields (as opposed to a random variable) to model uncertainty in the elastic modulus, and (2) the use of proper orthogonal decomposition (POD) to yield insight into the local factors that govern the global response of the panel, permitting enhanced response prediction based on the nature of the random field realizations.