analytical approach for thermo-electro-mechanical vibration of piezoelectric nanoplates resting on elastic foundations based on nonlocal theory

In the present work, thermo-electro vibration of the piezoelectric nanoplates resting on the elastic foundations using nonlocal elasticity theory are considered. in-plane and transverse displacements of the nanoplate have been approximated by six different modified shear deformation plate theories considering transverse shear deformation effects and rotary inertia. moreover, two new distributions of transverse shear stress along the thickness of the nanoplate were introduced for the first time. the equations of motion were derived by implementing hamilton’s principle and solved using analytical method for various boundary conditions including ssss, csss, cscs, ccss and cccc. based on a comparison with the previously published results, the accuracy of the results was confirmed. finally, the effects of different parameters such as boundary conditions, variations of the thickness to length ratio, aspect ratio, increasing temperature, external voltage, foundation coefficients and length scale on the natural frequency of the plate were shown and discussed in details.