Small scale thermal analysis of piezoelectric–piezomagnetic FG microplates using modified strain gradient theory

Free vibration and buckling analyses of the magneto-electro-elastic functionally graded (MEE FG) microplates in thermal environment are investigated for the first time. The MEE FG microplate is composed of two phases: piezoelectric (barium titanate) and piezomagnetic (cobalt ferrite) materials, which are distributed across the thickness direction based on the power law model. To satisfy Maxwell’s equation in the quasi-static approximation, the electric and magnetic fields are assumed a combination of trigonometric and linear functions across the plate thickness. To capture small effects on microstructures, the modified strain gradient theory (MSGT), including three length scale parameters combined with the generalized higher-order shear deformation theory (HSDT), is presented. The equilibrium equations for free vibration and buckling analyses of MEE FG microplates are derived by using Hamilton’s principle. Through those equations, the natural frequency and critical buckling load of MEE FG microplates are computed by using isogeometric analysis (IGA). Based on the Non-uniform rational B-splines (NURBs) basic functions, which achieve any desired degree of continuity of basis functions, the IGA easily satisfy the MSGT model’s higher-order derivatives. The advantage and accuracy of the proposed model are demonstrated through comparisons between the present results and those provided in the literature. The effect of the electric voltage, magnetic potential, power index, geometrical parameter and length scale parameters on the dimensionless frequencies and critical buckling loads of the MEE FG microplates is fully reported. The article’s results can be considered as benchmark solutions for the vibration and buckling of MEE FG microplates and they are helpful for manufacturing sensors, actuators, stability control, etc.