English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we present the analysis of stability for a piezoelectric beamsubject to a thermal law (Coleman-Gurtin or Gurtin-Pipkin thermal law) addingsome viscous damping mechanism to the electric field in $x-$direction and$z-$direction, and we discuss several cases. Then, there is no need to controlthe electrical field components in $x$-direction and $z-$ direction toestablish an exponential decay of solutions when the beam is subjected to aColeman-Gurtin law, otherwise a polynomial stability is established withGurtin-Pipkin thermal law in case when the electrical field components aredamped.

Stabilization of piezoelectric beam with Coleman-Gurtin or Gurtin-Pipkin thermal law and under Lorenz gauge condition