Nonlinear Flutter Analysis of Orthotropic Laminated Thin Rectangular Plates

Abstract

Abstract. This article focuses on the nonlinear flutter behaviors of laminated orthotropic thin rectangular plates under the influence of aerodynamic loading. The aerodynamic load is determined by the first-order piston theory. Applying Reddy's shear deformation plate theory, Hamilton's principle, and the Galerkin method, a set of ordinary differential equations (ODEs) can be derived. Besides solving the set of linear ODEs as an eigenvalue problem, the other more general nonlinear ODEs is solved numerically via the pseudo-arclength continuation algorithm. The present approach is validated by comparison with the published benchmarks. For linear flutter, the particular locking phenomenon is found when flutter occurs. For nonlinear flutter, the limit cycle oscillation (LCO) appears after the Hopf bifurcation points, and its amplitude exhibits significant growth for increasing dimensionless dynamic pressure. Some stable solutions are found before the critical flutter, thus demonstrating physical phenomena not captured in the linear analysis. The fact that the actual flutter boundary is lower when nonlinearity is present underscores the crucial importance of geometric nonlinearities for an accurate stability assessment. With increasing dimensionless dynamic pressure, quasi-periodic oscillation occurs. It is also observed that the complexity of LCO increases, which can be attributed to the appearance of numerous and nonunique quasi-periodic frequencies owing to the increased dimensionless dynamic pressure.