Vibration and flutter analysis of piezoelectric plates in an electrothermal field using higher order theories

In this study, we investigate the vibration and dynamic stability of a thick rectangular plate that is restrained on four edges by simple clamps. Nonlocal elasticity based on high‐order shear theories is used to model the structure, which takes into account not only shear flow along the thickness, but also different distributions of shear deformations. The inclusion of rotational inertia also significantly impacts the accuracy of the results. The aerodynamic flow on the plate surface is modeled using the linear piston theory, which relates the incoming load from the aerodynamic flow to the transversal deformation of the plate. By utilizing Hamilton's principle, the governing equations for the system are obtained and solved using the weighted residual method. The results are validated by comparing them to previous studies. The effects of various parameters, such as the plate's geometrical properties, the impact of different theories, heat, electric voltage, and nonlocal variables, on the vibration and flutter behavior of the plate are examined. Additionally, it is found that the application of negative voltage increases the critical aerodynamic pressure by creating a traction force, and that a suitable thermal load can avoid instability caused by aerodynamic load. By applying voltage and heat, it is possible to increase the flutter threshold and delay it.