Nonlinear Model Reduction of von Kármán Plates Under Linearized Compressible Fluid Flow

Abstract

Areduced ordermodel (ROM) of linearized compressiblefluidflowcoupledwith a vonKarmanplate is developed. SeparateROMs for both thefluid and structure are derived and are coupled through a solidwall boundary condition at the interface boundary. The structural ROM is formulated using the method of quadratic components, which postulates that the full kinematics of the plate can be represented using linear and quadratic terms. The fluidROM is constructed via a proper orthogonal decomposition method. Both ROMs are further reduced via a Galerkin discretization, and the coupled system is implicitly integrated in time. The coupled model is subsequently compared with previously validated models that used either a linearized plate model with the linearized compressible fluid model or a quasi-static fluidmodel with the vonKarman platemodel. The comparisons are conducted in high-Machnumber regimeswhere the comparison is admissible, and excellent agreement is found. Analysis of the resulting limit cycles shows two sets of discontinuities in the limit cycle amplitudes. These discontinuities have two salient features: a snap through phenomenon in phase space is observed in the higher modes, and the coalescing of several of the lower modes is observed below the critical dynamic pressures followed by a sudden separation above the critical dynamic pressures.