Effects of Elastically Supported Boundaries on Flutter Characteristics of Thin-Walled Panels

In order to investigate flutter characteristics of thin-walled panels with elastically supported boundaries, a method for dealing with the stiffness matrix constraint relationship is developed based on penalty functions. Combined with the first-order piston theory, flutter velocities and frequencies of thin-walled panels with the different cases of elastically supported boundaries are calculated. Firstly, a thin-walled panel is discretized by the finite element method, and springs with real stiffness coefficients are introduced to simulate elastically supported boundaries. Then, the pressure difference between the outer and inner surfaces of the panel and modal aerodynamic expressions are obtained by introducing the first-order piston theory. Finally, flutter equations are obtained in the time domain by combining the structural dynamic equations with the modal aerodynamic forces. Subsequently, they are transformed to the frequency domain at the flutter state. Then, flutter characteristics of the panel are obtained using the U-g method. The results show that the existence of elastically supported boundaries may reduce the flutter velocity and flutter frequency of the panel but can be enhanced and recovered through some appropriate damping configuration schemes. Calculating the flutter characteristics of thin-walled panels under elastically supported boundaries can more accurately simulate real supported situations and result in a safer design scheme for thin-walled panel structures.