Equations of high-frequency vibrations of porous piezoelectric plates

Dokmeci M., Altay G.

Symposium on Electro-Magneto-Mechanics, Virginia, United States Of America, 23 - 28 June 2002, pp.229-247 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • City: Virginia
  • Country: United States Of America
  • Page Numbers: pp.229-247
  • Istanbul Technical University Affiliated: No


To predict their physical response at high-frequency vibrations, a system of 2-D approximate equations is consistently derived for thin porous piezoelectric plates. First, a porous field vector (i.e., the gradient of the void volume fraction field) is introduced as a new concept that is analogous to the electric field and thermal field vectors. With its use, the principle of virtual work is expressed for a porous piezoelectric continuum and a three-field variational principle is obtained. The variational principle is augmented through Friedrichs's transformation so as to formulate a unified variational principle. Next, by use of this principle together with the series expansions of the field variables in the thickness coordinate of plates, the system of higher-order equations is formulated in invariant, variational as well as differential forms. The system of higher-order equations governs the extensional, thickness-shear and flexural and also coupled vibrations of porous piezoelectric plates at both low and high frequencies. Lastly, the plate equations are shown to agree with and to recover some earlier ones, and the uniqueness in their solutions is investigated.