Study On Nonlinear Dynamics Of Axially Moving Flexible Electronic Thin Films

Flexible electronic thin films are widely used in aerospace,energy,medical,and other fields.During the preparation process of flexible electronic thin films,they are often subjected to complex working conditions,resulting in complex dynamic behaviors of the system.To improve the preparation efficiency and quality,and ensure that the film works under stable conditions,it is of great significance to explore the dynamic characteristics of flexible electronic films.This paper aims to study the dynamic characteristics of transverse free vibration,longitudinal free vibration,and transverse nonlinear forced vibration of axially moving flexible electronic films.The main objectives of this study are as follows:(1)The transverse vibration characteristics of an axially moving flexible electronic film are investigated in this study.The electric field model is introduced based on Maxwell’s equations,and the expression of the electric field force is derived.The differential equation of motion is obtained using the Hamiltonian principle,and it is further transformed into a dimensionless vibration mode differential equation.The differential quadrature method is used to solve the problem,considering the boundary condition that the opposite side is almost free.The influence of the dimensionless electric field force,tension ratio,and aspect ratio on the dimensionless complex frequency of the system is analyzed.The results indicate that the dimensionless electric field force directly affects the critical instability velocity of the system.The larger the dimensionless electric field force,the smaller the instability critical velocity.The aspect ratio and tension ratio do not affect the instability critical velocity of the system.However,the smaller the aspect ratio or tension ratio,the smaller the instability interval,and the sooner the system returns to a stable state.(2)The longitudinal vibration characteristics of an axially moving flexible electronic film are investigated in this study.The vibration differential equation of the system is deduced based on D’Alembert’s principle,and it is further transformed into a dimensionless vibration mode differential equation.The four-sided simply supported boundary conditions are considered,and the equation is solved by an analytical method to obtain the expression of the system’s natural frequency.The relationship diagram of the system’s dimensionless complex frequency versus dimensionless velocity is analyzed to discuss the effects of the dimensionless electric field force and aspect ratio on the longitudinal vibration characteristics of the system,and compared with the transverse vibration.The results indicate that neither the dimensionless electric field force nor the aspect ratio affects the critical velocity of the system instability.The greater the dimensionless electric field force,the larger the instability interval of the system.The larger the aspect ratio value,the later the system returns to stability,and the larger the instability interval.The instability interval of longitudinal vibration is within the instability interval of transverse vibration.(3)Building upon the study of the transverse vibration characteristics of the system,this paper analyzes the dynamic characteristics of the transverse nonlinear forced vibration of the axially moving flexible electronic film.The Kelvin-Voigt viscoelastic model is introduced,and the Galerkin method discrete equation is used to transform the partial differential equation into an ordinary differential equation.The equation of state is solved numerically to obtain the bifurcation diagram,phase diagram,and Poincare cross-sectional diagram of the thin film system.The influence of the dimensionless electric field force,the amplitude of external excitation force,aspect ratio,and dimensionless velocity on the dynamic characteristics of transverse nonlinear vibration of the system is analyzed.