Journal of Stress Analysis Vol. 4, No. 1, Spring − Summer 2019 Efects of Couple-stress Resultants on Thermo-electro-mechanical Behavior of Vibrating Piezoelectric Micro-plates Resting on Orthotropic Foundation K. Khorshidi * , M. Ghasemi, M. Karimi, M. Bahrami Department of Mechanical Engineering, Arak University, Arak, Iran. Article info Article history: Received 10 July 2019 Received in revised form 08 September 2019 Accepted 14 September 2019 Keywords: Couple-stress theory Analytical approach Orthotropic foundation Piezoelectric micro-plate Abstract This work aimed to study the thermo-electro vibration of a piezoelectric micro-plate resting on the orthotropic foundation. To catch the small-scale efects of the structure, couple-stress theory was employed. Motions of the structure were modelled based upon diferent shear deformation theories including exponential, trigonometric, hyperbolic, parabolic, and ffth-order shear deformation theories. These modifed shear deformation theories are capable of considering transverse shear deformation efects and rotary inertia. Equation of motions are derived with Hamilton’s principle and to solve these equations an analytical approach is applied. Besides, Efect of diferent boundary conditions including SSSS, CSSS, CSCS, CCSS and CCCC are investigated. The present results are validated with the previously published results. In the result section, the infuences of various parameters such as increasing temperature, boundary conditions, foundation parameters, thickness ratio, aspect ratio, external voltage and length scale on the natural frequencies of the plate are illustrated in detail. Nomenclature a Length of the plate σ ij Normal stresses b Width of the plate m ij Couple stress tensor h Thickness of the plate χ ij Curvature tensor E Young’s modulus E i Electric feld ν Poisson’s ratio D Electric displacement ρ Mass density G Shear modulus u Displacement in the x direction ℓ Material length scale parameter v Displacement in the x direction F Axial force w Displacement in the x 3 direction K gx Shear foundation parameter T Kinetic energy of the plate K gy Shear foundation parameter U Strain energy of the plate K w Winkler constant W Work done by external forces c d Damping constant δ Variation operator θ Angel of orthotropic function ω Natural frequency of the plate V 0 External electric voltage ε ij Normal strains Φ Electric potential * Corresponding author: K. Khorshidi (Associate Professor) E-mail address: k-khorshidi@araku.ac.ir http://dx.doi.org/10.22084/jrstan.2019.19583.1097 ISSN: 2588-2597 125