This article explores the dynamic characteristics of a specific plate known as 'double-variable-edge' (DVE) plate with varying thickness, constructed from functionally graded porous material. The edge profiles of the plate and its thickness variation are defined by optional mathematical functions (polynomial and arc functions are chosen in this paper). The nonlinear dynamics of the double-variable-edge and variable thickness (DVEVT) plate, encompassing periodic and chaotic behaviors, have been investigated utilizing classical plate theory, incorporating the Von Karman-Donnell geometrical nonlinearity assumption, and employing Galerkin's method. Furthermore, this paper examines the linear characteristics by assessing fundamental frequencies. To establish the reliability of this approach, the linear frequencies and nonlinear curves are validated against prior literature and Finite Element Analysis (FEA). Additionally, the study reveals the emergence of chaotic phenomena, as evidenced by the phase plane and Poincaré map, which become increasingly pronounced as the external load approaches the critical load. This critical load point signifies the juncture at which the structural behaviors transitions into a state of chaos. This research is anticipated to unlock significant potential within the aerospace, mechanical, and construction engineering, particularly for structures characterized by intricate profiles and varying thicknesses.