Journal
ARCHIVE OF APPLIED MECHANICS
Volume 83, Issue 4, Pages 495-507Publisher
SPRINGER
DOI: 10.1007/s00419-012-0698-1
Keywords
Stability; Viscoelastic plate; Follower force; Piezoelectric layer
Categories
Funding
- National Natural Science Foundation of China [11101330]
- Foundation for the Doctoral Program of Higher Education [20106118110006]
- Natural Science Foundation of Education Department of Shaanxi Province of China [11JK0535]
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The effects of a piezoelectric layer on the stability of viscoelastic plates subjected to the follower forces are evaluated. The differential equation of motion of the viscoelastic plate with the piezoelectric layer is formulated using the two-dimensional viscoelastic differential constitutive relation and the thin plate theory. The weak integral form of the differential equations and the force boundary conditions are obtained. Using the element-free Galerkin method, the governing equation of the viscoelastic rectangular plate with elastic dilatation and Kelvin-Voigt distortion is derived, subjected to the follower forces coupled with the piezoelectric effect. A generalized complex eigenvalue problem is 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 non-conservative viscoelastic plate. For the viscoelastic plate with various boundary conditions, the results for the instability type and the critical loads are presented to show the variations in these factors with respect to the location of the piezoelectric layers and the applied voltages. The stability of the viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.
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