Dynamic stability of an axially moving paper board with added subsystems

Abstract

Paper board with bending stiffness is usually used as the substrates on cigarette package printing industry. The vibration of these paper boards in high speed affects the printing precision. The dynamic characteristics and stability of moving paper board with finite interior elastic point supports and elastic edges restrained are investigated. First, the energy function of the system is established by using the extended Hamilton's principle; second, the dimensionless equations of motion for the moving paper board are obtained using the element-free Galerkin method. The equations of motion and the eigenvalue equations of the system are established. The relationship between the first three complex frequencies of the system and the moving speed is then obtained by the numerical calculation. The effects of the elastic point supports, the elastically restrained edges, and the dimensionless speed of the motion on the dynamic stability of the paper board are analyzed. The critical speed when the paper board is in a stable state under different conditions is obtained. The results improve the dynamic stability of the paper board in printing process and provide the theoretical basis for the optimization of printing equipment.

Thermoelastic Coupling Vibration and Stability Analysis of Rotating Annular Sector Plates

“…while the boundary conditions of free edge at the inner radius ( = ) and outer radius ( = ) are as follows. Substituting (20) into (21), and can be determined by the above boundary conditions, and then, and of the annular sector plate with the two radial edges having clamped or simply supported can be obtained.…”

“…The differential equation of thermoelastic coupling transverse vibration of the rotating annular sector plate is the fourth-order partial differential equation with variable coefficients. The high-order partial differential equation has been solved by the finite element method and Galerkin method in some literature [13,16,[18][19][20]. The differential quadrature method (DQM) was firstly proposed by Bellman and Casti in early 1970s [21].…”

Nonlinear forced vibration of a moving paper web with varying density

“…Yang et al 15 applied the finite element method to study the linear free vibration and nonlinear forced vibration of axially moving viscoelastic plates. Wang et al 16 studied the dynamic characteristics and stability of a paperboard with elastic point support and elastic edge constraint. The extended Hamilton principle was used to establish the equation of the system, and the meshless Galerkin method was used to discretize equation.…”

Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

“…Some research work on a high-order partial differential equation had been carried out by the Galerkin method and finite element method. 1,3,7,8,11,12,22 Yayli 23–27 used the Fourier sine series and Stoke transformation to analyze the high-order partial differential equation of vibration. The computation in these methods is complicated.…”