# Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric Layer:

Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric... The dynamic stability of the moving viscoelastic plate with the piezoelectric layer is studied. On the basis of the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer in the Laplace domain is formulated, the equation is suitable for various viscoelastic differential models. Then, the differential equation of motion of the viscoelastic plate with elastic dilatation and Kelvin–Voigt distortion in time domain is derived, with the piezoelectric effect. The complex eigenvalue equations of axially moving viscoelastic plate are established by the differential quadrature method. The generalized eigenvalue equations are solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the axially moving viscoelastic plate. Via numerical calculation, the results for the instability type and the corresponding critical moving speed of viscoelastic plate are presented to show the variations in these factors with respect to the dimensionless moving speed, the dimensionless delay time and the applied voltages. The dynamic stability of the axially moving viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Low Frequency Noise, Vibration and Active Control SAGE

# Dynamic Characteristics and Stability of Axially Moving Viscoelastic Plate with Piezoelectric Layer:

, Volume 33 (3): 15 – Sep 1, 2014
15 pages      /lp/sage/dynamic-characteristics-and-stability-of-axially-moving-viscoelastic-Rk1sqnuvMV
Publisher
SAGE
ISSN
2048-4046
eISSN
2048-4046
DOI
10.1260/0263-0923.33.3.341
Publisher site
See Article on Publisher Site

### Abstract

The dynamic stability of the moving viscoelastic plate with the piezoelectric layer is studied. On the basis of the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer in the Laplace domain is formulated, the equation is suitable for various viscoelastic differential models. Then, the differential equation of motion of the viscoelastic plate with elastic dilatation and Kelvin–Voigt distortion in time domain is derived, with the piezoelectric effect. The complex eigenvalue equations of axially moving viscoelastic plate are established by the differential quadrature method. The generalized eigenvalue equations are solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the axially moving viscoelastic plate. Via numerical calculation, the results for the instability type and the corresponding critical moving speed of viscoelastic plate are presented to show the variations in these factors with respect to the dimensionless moving speed, the dimensionless delay time and the applied voltages. The dynamic stability of the axially moving viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.

### Journal

Journal of Low Frequency Noise, Vibration and Active ControlSAGE

Published: Sep 1, 2014

Keywords: Dynamic Characteristics,Stability,Moving viscoelastic plate,Piezoelectric layer,Differential Quadrature method