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 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 functionally graded piezoelectric (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 equations of motion and stability are governed using Hamilton's principle, and both mechanical and electrical field variables are incorporated. For an accurate numerical solution, the differential quadrature method (DQM) is employed, allowing the use of Lagrange interpolated polynomials defined at discrete grid points based on Chebyshev polynomial roots to approximate spatial derivatives. This results in rapid convergence and energy-efficient computations. A novel layer-wise modeling method is additionally proposed in order to accurately portray the through-thickness variation of mechanical and electrical fields, which is critical for piezoelectric materials exposed to high-frequency electrical shocks. In forced vibration analysis, the Laplace transform is done on the time-dependent governing equations, thus allowing the computation of transient dynamic responses that are induced by electrical shock excitation. The results unfold in detail the variations in the effect of gradation, electrification, and geometry on the stability limits, frequencies, and characteristics of the dynamic response of FGP plates. The suggested method provides a dependable theoretical and numerical basis for the creation of sophisticated piezoelectric structures in mechanical welding and other smart manufacturing applications.