Exact solution of post-buckling behavior of porous piezoelectric nanobeams with surface effects

Piezoelectric nanobeams are important components in micro-nano electromechanical systems. They are often used as mechanical structures such as wireless sensors, biological probes and transistors. And their mechanical performance is a very important research topic. Based on the theory of surface elasticity and the "core-shell" model, post-buckling behavior of porous piezoelectric nanobeams is analyzed using the first-order shear deformation beam theory, where the surface effect is introduced by employing the surface energy model. The governing equations and boundary conditions of post-buckling of porous piezoelectric nanobeams under mechanical loading were derived by introducing the concept of median surface in physics and the principle of minimum potential energy. The influence of surface effect on post-buckling configuration, post-buckling path, amount of induced charge and critical load of porous piezoelectric nanobeams with different external constraints and porosities were discussed. The results show that considering surface effects, the effective elastic modulus and critical load of porous piezoelectric nanobeams will be increased, and the post-buckling configuration, post-buckling path and amount of induced charge will be reduced. Meanwhile, the mechanical properties of porous piezoelectric nanobeams can be effectively improved by appropriate pore distribution. These findings can be used as a theoretical basis for the accurate design and manufacture of micro-nano mechanical and electronic devices.