Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

et al. 2019

Shock and Vibration

Nonlinear vibration characteristics of a moving membrane with variable velocity have been examined. The velocity is presumed as harmonic change that takes place over uniform average speed, and the nonlinear vibration equation of the axially moving membrane is inferred according to the D’Alembert principle and the von Kármán nonlinear thin plate theory. The Galerkin method is employed for discretizing the vibration partial differential equations. However, the solutions concerning to differential equations are determined through the 4th order Runge–Kutta technique. The results of mean velocity, velocity variation amplitude, and aspect ratio on nonlinear vibration of moving membranes are emphasized. The phase-plane diagrams, time histories, bifurcation graphs, and Poincaré maps are obtained; besides that, the stability regions and chaotic regions of membranes are also obtained. This paper gives a theoretical foundation for enhancing the dynamic behavior and stability of moving membranes.

Section: Introductionmentioning

confidence: 99%

Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

et al. 2019

Shock and Vibration

“…The conclusion is that critical divergence and restabilization speed of the first-order mode decrease with the increase of thermal parameters. Tang et al [6] examined the vibration and dynamic stability of axially viscoelastic plates with variable tension by using the method of multiple scales and the Routh-Hurwitz criterion. Robinson and Adali [7] investigated the influence of the thickness ratio and the cross-section on the vibration of in-plane moving viscoelastic plates.…”

Section: Introductionmentioning

confidence: 99%

Transverse Vibration of a Moving Viscoelastic Hard Membrane Containing Scratches

Mathematical Problems in Engineering

et al. 2019

The transverse vibration and stability of a moving viscoelastic hard printing membrane containing scratches are investigated. Based on the viscoelastic differential constitutive relation, thin plate theory, and d' Alembert principle, the differential equation of a moving viscoelastic hard membrane with a straight scratch through the surface is derived by using the continuity condition of the scratches. The complex characteristic equation is obtained by using the differential quadrature method. The effects of the scratch depth and scratch position on the critical instability speed of the moving hard membrane were highlighted by solving the differential equation and numerical calculation, and the coupling effects of speed and scratch depth on vibration characteristics of the hard membrane are also analyzed. Numerical calculation results show that the hard membrane experiences divergence instability when the actual printing speed is v=23.2 m/s, and the membrane is stable when v<23.2 m/s. The theoretical guidance and method for scratches detection of the precision coated hard membrane are provided.

“…Yuan et al 11 studied precise solutions with regard to non-axisymmetric vibrations of radially inhomogeneous circular Mindlin plates with variable thickness. The method of multiple scales was used by Tang et al 12 to study the dynamic stability of accelerated plates with longitudinally varying tensions. The translating speed, aspect ratio, and boundary conditions had significant effects on the free in-plane vibration, and the out-of-plane vibration of a moving membrane was investigated by Shin et al 13,14 Banichuk et al 15 studied the dynamics and stability of a moving web subjected to tension that was not homogeneous.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration and stability of a moving printing web with variable density based on the method of multiple scales

Journal of Low Frequency Noise, Vibration and Active Control

et al. 2019

An axially moving printing web with variable density in a printing process causes a geometric nonlinear vibration, and a nonlinear vibration system is established using the von Karman nonlinear plate theory and the D'Alembert principle. The time and displacement variables are separated using the Galerkin method. The ordinary differential equation of a web is solved using the method of multiple scales. The amplitude-frequency response equation of a moving web is obtained. The time histories, phase-plane portraits, and amplitude-frequency curves of the system are obtained by numerical calculations. The influence of different dimensionless speeds and variable density coefficients on the nonlinear vibration characteristics of the printing web is analyzed. The results show that the overprinting accuracy can be ensured by making a reasonable choice of web speed in the stable region.