Nonlinear vibration characteristics and stability of the printing moving membrane

Abstract

Most studies on the membrane vibration are limited to discussing small deflection linear problems, but rarely on the study of nonlinear large deflection problems. In practice, however, membrane deflection is not necessarily far less than the thickness, so it is necessary to research the large deflection vibration problems of moving membrane. In this paper, the large deflection vibration characteristics and stability of the moving printing membrane are analyzed. Large deflection vibration equation of an axially moving membrane is derived by using Von Karman nonlinear plate theory. The large deflection vibration of rectangle moving membrane with four edges fixed boundary is studied by using the Bubnov-Galerkin method which is a semi-analytical-weighted residual method, and the large deflection vibration complex frequency curves along with the change of speed and aspect ratio in the different initial conditions are obtained. The results show that the large deflection nonlinear vibration can be effectively avoided by increasing membrane aspect ratio and decreasing the membrane dimensionless velocity. The study provides theoretical basis for improving the operation stability of the printing equipment.

General Formulation for Free Vibration of Elastic Solids with Static Loads and Application to Rotating Tapered Cantilever Beam Vibration 

“…Comparing equation (9) with (2) shows that they both have a second order term except equation 9is a forced dynamical system while equation 2is unforced. Therefore, it can be proved that like equation (2), equation (8) will not have a vibration frequency too.…”

“…For a nonlinear dynamic system, due to complicity, there never was a universal theory or algorithm available to tell whether it has a natural vibration frequency, to tell whether it has a unique solution, and to tell what the forced response is. Although the Rayleigh-Ritz method [6][7][8][9][10][11][12] was applied by scientists and engineers to compute eigenvalues or frequencies for specific individual problems successfully, it was never indicated explicitly how a nonlinear dynamic system should be assessed. Compared with a linear system, a nonlinear dynamic system is complicated.…”

“…In literature, many simple methods were developed to assess natural frequencies of a nonlinear system using perturbation technique, for example, Thomas et al [18], Bokain [19], Luo [3][4][5] and Naguleswaran [7] all investigated the vibration frequencies of the beam-type structures subjected to external static loads using different methods. With use of the von Karman nonlinear plate theory, Wu et al [8] proposed a method to predict the vibration of nonlinear moving printing membrane with a large deformation, but this method is invalid for a solid, while Marynowski [9] used a directly numerical solution to investigate the frequencies of moving paper wed with pre-stress. Perturbation analysis was used to extract frequencies of every nonlinear dynamic system by all the current commercial software today.…”

Lateral vibration analysis of monatomic chains considering atomic longitudinal displacement

“…17,18 The large deflection vibration characteristics and stability of the moving printing membrane were analyzed. 19 The authors proposed a new scheme that relies on the nonlinearity, which utilizes nonlinear time history analysis results. 20 However, the microscopic origin of the damping lies in localized defect states in the material and degrades the quality factor.…”

Nonlinear analysis and simulation of active hybrid aerodynamic and aerostatic bearing system

“…Thus, there is little wear between the rotor and the bearing, which results in longer spindle system life. 1,2 Gas is also compressible, has very low value of viscosity, which means it has very little fluid shear and does not require much power to achieve very high rotation speed. This means that the bearing does not heat up easily, and can operate in a high temperature environment without affecting its dynamic performance.…”