Size-Dependent Thermomechanical Vibration Analysis of Porous Functionally Graded Magneto–Electro–Elastic Nanoplates within a Nonlocal Strain-Gradient Framework

Abstract In this study, a size-dependent thermomechanical vibration theory for porous functionally graded magneto-electro-elastic (FG-MEE) nanoplates in the hybrid nonlocal strain gradient theory is proposed. The formulation accounts for temperature rise, electroelastic, and magnetostrictive coupling effects in conjunction with nonlocal and strain gradient effects. The gradations in the material properties in the direction transverse to the plate are described using a power law distribution. The formulation is based on Hamilton’s principle. The final governing equation is solved using a harmonic exponential method to obtain an eigenvalue problem. The results are presented in terms of a dimensionless frequency parameter. The influence of porosity index and porosity distribution patterns (FOAM I, FOAM II, and FOAM III) in conjunction with material gradations on the dimensionless frequency parameter is presented in detail. The results show that an increase in porosity index reduces the frequency. The degradation in frequency is found to depend sensitively on the porosity distribution patterns. FOAM I shows the maximum degradation in frequency and approaches complete failure at a lower value of temperature rise. An increase in temperature reduces the frequency. The nonlocal theory shows a stiffness degradation tendency. The stiffness degradation tendency increases with an increase in temperature. The magnetic actuation is found to increase the stiffness and delays degradation. The electric actuation can cause degradation depending upon the dominance of the active phase. The elevated temperature cases are presented to show the stability tendency. In practice, it should be noted that the Curie temperature should be taken into consideration to ensure functionality.