Abstract: “In this study, a functional for the dynamic analysis of viscoelastic Kirchhoff plates is obtained through an efficient systematic procedure based on the Gâteaux Differential Method. For the solution of the derived functional, mixed finite element method in transformed Laplace-Carson space is used. In this functional, there exists four independent variables such as deflection (w), internal forces (Mx, My, Mxy) in addition to the dynamic and geometric boundary condition terms. For modeling the viscoelastic behavior, four parameter solid model is employed. For transformation of the solutions obtained in the Laplace- Carson domain to the time domain, different numerical inverse transform techniques are employed. The developed solution technique is applied to several dynamic example problems for the verification of the suggested numerical procedure.”

Keywords: dynamic analysis, viscoelastic plates, Gâteaux differential, mixed finite element method, Laplace-Carson transform