The Nonlinear Dynamical Analysis of a Sandwich Plate with In-Plane Loading in Supersonic Flow

Abstract

Nonlinear dynamics of a sandwich plate with viscoelastic soft core in supersonic flow are investigated by considering the in-plane periodic loading. Using Reddy’s third-order shear deformation theory and von Karman’s nonlinearity, the governing partial differential equations are derived by Hamilton’s principle and then truncated into a set of ordinary differential equations by Galerkin method. The critical speed for flutter is discussed by employing the linear theory. Further, the method of multiple scales is used in the nonlinear dynamical analysis of the truncated system. The Poincaré map is numerically calculated to identify dynamical behaviors. The bifurcation diagrams are presented for varying the dimensionless in-plane loading fluctuation amplitude and the Mach number related dimensionless parameter while other parameters are unchanged.