Supersonic Aerothermoelastic Nonlinear Flutter Study of Curved Panels: Frequency Domain

Abstract

T HIS Note is a continuation of the study [1] that addresses the development of a finite element (FE) formulation and a corresponding solution procedure to investigate the nonlinear supersonic aerothermoelastic flutter response of curved panels. In this Note, a finite element time-domain method is presented for studying the pre/post-flutter-onset behavior of curved panels subjected to a simultaneous aerodynamic and thermal loading. The raised skin temperature, which is a characteristic part of the supersonic flight regime, induces thermal in-plane forces and transverse bending moments, which may cause many instabilities such as the preflutter buckling/bowing, limit cycle oscillations, periodic and nonperiodic dynamic motion, and chaos. A frequencydomain solution of the flutter phenomenon accurately predicts the panel behavior till the flutter onset, however, it lacks the capability to predict the post-flutter-onset panel response. Hence, the work presented in this Note aims at developing a computationally costeffective time-domain solution procedure for supersonic nonlinear post-flutter-onset analysis of curved panels. The formulation in this overall study is based on the building blocks of the vonKarman nonlinear strain-displacement relation, the Marguerre curved-plate theory, the first-order shear deformation theory, the quasi-steady piston theory, and the quasi-static thermoelasticity. In the time-domain part of the solution scheme, a finite element procedure is developed to predict the preflutter and, most important, the post-flutter-onset panel response. The system equations of motion (EOM) in structural degrees of freedom (DOF) are transformed into modal coordinates and solved by a fourth-order Runge–Kutta numerical scheme. Time-history responses, phase plots, power spectral density plots, and bifurcation diagrams are studied for a better understanding of the fluttering curved-panel system. II. Finite Element Formulation and Solution Procedure