Instability And Nonlinear Vibration Of Orthotropic Moving Thin Films

Flexible films have broad application prospects in artificial intelligence,national defense,biomedicine,and other fields due to their lightweight and flexible nature,as well as high surface tension.However,this type of special functional film product has been unable to break through the limitations of large-scale and high-throughput commercial applications.On the one hand,it is related to current printing technology,and on the other hand,the complex working conditions encountered by the film in the actual printing process lead to complex nonlinear dynamic behavior,resulting in insufficient mechanical stability and easy tearing,wrinkling,and other problems in the production and preparation process.This not only limits the production efficiency of thin film products,but also causes a waste of resources.Therefore,from the perspective of dynamics,it has certain scientific significance and engineering value to explore the main factors that cause the instability of the film,so as to optimize the relevant parameters and improve the production efficiency.The main work of this article includes:(1)The influence of system parameters of orthotropic moving thin films under fluid solid coupling on the aeroelastic instability of the moving thin film system and the stability of periodic solutions of the thin film system is studied.Based on the quasi Hamilton’s principle and Von Karman’s large deflection theory,the nonlinear dynamic differential equation of the system is derived.The Ritz-Galerkin method is used to solve the dimensionless equation integrally,and the harmonic balance method is used to obtain the analytical approximate solution.On this basis,the influence of various parameters in the film system,such as film motion speed,length width ratio,etc.on the critical unstable airflow velocity of the system is analyzed,and the stability of the periodic solution of the system is discussed by analyzing the characteristics of the system frequency response curve.(2)The influence of system parameters on the aeroelastic instability and periodic solution stability of the orthotropic moving thin film system with oblique support under fluid solid coupling is studied.By converting the straight oblique coordinate system,the nonlinear dynamic differential equation considering oblique support is obtained.After dimensionless equation,the Ritz-Galerkin method is used to integrate and simplify dimensionless equation,and harmonic balance method is used to obtain analytic approximate solution.Focus on analyzing the influence of oblique support angle on the aerodynamic instability of the system and its impact on the stability of the periodic solution of the system.(3)The bifurcation and chaos of orthotropic moving thin films under thermoelastic coupling are studied.Based on the quasi Hamilton’s principle,the nonlinear differential equation of motion of the film system is derived,and the Ritz-Galerkin method is used to solve dimensionless equation integrally.The state equation is solved by the fourth order Runge-Kutta method,and the bifurcation diagram,phase diagram,Poincare section diagram,and displacement time history diagram of the film system are obtained.The influence of system parameters such as elastic modulus ratio,Aspect ratio,dimensionless velocity,dimensionless temperature force on bifurcation and chaos of moving film system is analyzed,and the stable working range and divergent instability range of moving film are obtained.