Extraction of the governing equations for steady state and axisymmetric behavior of a porous piezoelectric circular solid plate

Subject Areas : Smart & Advanced Materials

علی ابجدی ¹ , محسن جباری ² , احمد رضا خورشیدوند ³

1 - گروه مهندسی مکانیک، واحد تهران جنوب، دانشگاه آزاد اسلامی، تهران، ایران
2 - South Tehran Branch, Islamic Azad University, Tehran, Iran
3 - گروه مهندسی مکانیک، واحد تهران جنوب، دانشگاه آزاد اسلامی، تهران، ایران

Received: 2021-06-12 Accepted : 2021-06-12 Published : 2020-11-01

Keywords: Circular solid plate, Governing equations, Porous piezoelectric materials, Piezothermoelastic behaivior, Linear elasticity theory,

Abstract :

Based on the available evidence, porous piezoelectric materials have great potential for the development of smart (active) structures with high strength, high stiffness and light weight such as ceramics and composites. Among the ceramic materials with porous piezoelectric compounds, can be mentioned Lead-zirconate-titanate (PZT), Lead-titanate (PbTiO2), Lead-zirconate (PbZrO3), Barium-titanate (BaTiO3), Cadmium-selenide (CdSe), etc. This study extracts the governing partial differential equations for steady- state and axisymmetric behavior of a circular solid plate is made of an undrained saturated porous piezoelectric hexagonal material symmetry of class 6 mm. The porosities of the plate vary through the thickness; thus, material properties, except poisson’s ratio, are assumed as exponential functions of axial variable z in cylindrical coordinates. Additionally, piezothermoelastic behavior of a circular plate subject to external thermal, mechanical and electrical loads is considered, so various concepts including three-dimensional linear elasticity theory and dielectric theory are used in combination to create a linear piezoelectric model. The extraordinary and special industrial properties of porous piezoelectric materials, their increasing use and the need to know the behavior of these materials, doubles the importance of this research.