Structural Stability and Dynamic Characteristics of Functionally Graded Piezoelectric Plates Subjected to Electrical Shocks for Future Mechanical Welding Applications

The research presented here delves into the functionally graded piezoelectric (FGP) plates’ structural stability and the dynamic properties under shock electrical loading, considering the future mechanical welding application of such materials. A higher-order shear deformation theory (HSDT) is utilized to precisely depict the phenomenon of transverse shear deformation without the necessity of shear correction factors. The electrical conductivity, dielectric constant, and piezoelectric coefficients of the FGP plate are presumed to vary non-uniformly through the thickness according to a combined half-cosine and linear distribution dictated by Maxwell’s equations to facilitate realistic electromechanical coupling. The motion and stability equations are described through Hamilton’s principle, which includes both mechanical and electrical field variables. The differential quadrature method (DQM) is used for an exact numerical solution, permitting the Lagrange interpolated polynomials to be used for the approximation of spatial derivatives at discrete grid points based on the roots of Chebyshev polynomials. This leads to efficient and quick computations as well as sorcery in convergence. A new layer-wise modeling approach is also put forward to accurately depict the through-thickness variation of mechanical and electrical fields, which is very important for piezoelectric materials subjected to high-frequency electrical shocks. In the analysis of forced vibrations, the temporal governing equations undergo Laplace transforms, thus granting the calculation of dynamic responses that are transient and excited electrically. The results unravel the effect of gradation, electrification, and geometry on the stability limits, frequencies, and characteristics of the dynamic response of FGP plates in great detail. The proposed approach is a reliable theoretical and numerical foundation for the development of advanced piezoelectric structures in mechanical welding and other smart manufacturing applications.