The Flutter Analysis Of Sandwich Panel Based On Complex Modal Method

This paper established a physical model of two-dimensional single wall plate withsupersonic aerodynamic force loading on one side. Based on the Hamilton’s principle theequilibrium equation was built. The plate’s flutter critical Mach number was determined bythe Galerkin method and the aerodynamic force was calculated by the one order piston theory.By considering the nonlinear term,the plate’s vibration mode and response before and afterflutter was analyzed by Runge-Kutta method. Then a physical model of two-dimensionalsandwich wall plate with supersonic aerodynamic force loading on one side was established.According to the Daranber’s principle, the balance equation was setted up. The sandwich wallplate’s flutter critical Mach number was determined by the Galerkin method and Complexmodal method and the two methods were compared.Considering the first four order modal,the first and the second order frequency coincided and make the vibration energy accumulatedto occurred flutter, and the complex modal method is more accurate. The study by usingComplex mode method found that,considering the viscoelasticity of the mid-layer, with theincrease of viscous damping, the critical flutter Mach number and the corresponding criticalflutter frequency of the system will decrease at first and then increase. It is concluded that thereason for this phenomenon is due to the dual effect of the viscous damping. The viscousdamping can reduce the natural frequency to make the system less stable on one hand, andabsorb energy which enhances the stability on the other hand. The system presents a complexphenomenon as the result of dual effects of the viscous damping. When the viscous dampingis very small, the former effect plays the leading role. As viscous damping increases, the lattereffect becomes more and more obvious.The conclusions of this research will be meaningful inthe design of composite panels in supersonic flow.