The Bifurcation Research In Panel Flutter Problem

This issue mainly researches the stability and bifurcation phenomena for the equilibriumabout two-dimensional flat-panel flutter issue (0,0) in the supersonic flow. And then we do amore detailed study in co-dimension three bifurcation on the basis of co-dimension twobifurcation, find the third unfolding parameters of co-dimension three bifurcation, get thenumeral of equilibrium point and domain of existence in the system, draw the respondingdiagrams by using the numerical calculation, and analyze the response in differentdisturbances.Firstly, premising that the sheet is in line with the Kelvin-Voigt viscoelastic assumptions,it deduces the differential equations of motion which governs the system, and lets itdimensionless by using the Von Karman theory of nonlinear equations of plate. Afterward, itdisperses the equation of motion into a four-dimensional ordinary differential equation(two-mode model) by using the Two-term Galerkin Method, obtaining the correspondingdegenerate system in the system. With the help of center manifold theory it further simplifiesthe system and calculates the center manifold of the system (two-dimensional ordinarydifferential equation). In succession, by using the normal form theory it further simplifies theequation of motion on the center manifold, eliminating the non-linear terms which does notaffect the motion character of the system，working out its normal form theory. At last, usingthe normal form theory, it researches the co-dimension three bifurcation, determining its thirdunfolding parameters and letting the equation dimensionless and re-measure again, getting thesystem equilibrium numbers and the presence of domain, and it does digital analysis onequilibrium point, getting the phase flow diagrams, and it does special analysis by combiningthe panel flutter problem.