This paper presents an analysis of the free vibration and nonlinear dynamic response of a complex-profiled nanocomposite plate (CPNP), akin to a car door plate. The materials utilized in this study comprise a core composed of carbon nanotube-reinforced nanocomposite (CNTRC), integrated with two face sheets made of magneto-electro-elastic materials \({\text{BaTiO}}_{3}-\text{ Co}{\text{Fe}}_{2}{\text{O}}_{4}\) . Four different types of carbon nanotube (CNT) distributions are considered for the core layer, while \({\text{BaTiO}}_{3}-\text{ Co}{\text{Fe}}_{2}{\text{O}}_{4}\) is incorporated in each face sheet, with a volume fraction set to 0.5. The distribution of reinforcements throughout the plate's thickness is assumed to be uniform and functionally graded. The plate features a rectangular shape with one edge that varies according to a mathematical function, such as a linear, exponential, or sinusoidal profile. Equations of motion, incorporating geometric nonlinearities defined by von Karman–Donnell and applying Galerkin’s method, are derived to obtain the dynamic and chaotic characteristics of the complex structure. The results obtained are validated against previous documents and finite element methods (FEM) to confirm the accuracy and reliability of the calculation method presented in this paper. The influence of material and geometrical parameters, as well as electro-thermo-magneto fields, are scrutinized within this study. The outcomes presented in this paper hold promise for applications in the aerospace, automobile, and mechanical industries.
