On the measurement of the nonlinear dynamics of sandwich sector plate surrounded by the auxetic concrete foundation: Introducing a machine learning algorithm for nonlinear problems

•Measuring nonlinear dynamics of sandwich rotary sector plate with nanocomposite reinforced face sheets.•Presetting centrifugal and Coriolis effects due to rotation on the nonlinear equations of the sandwich sector plate.•Presenting auxetic concrete foundation due to increasing the stiffness and stability of the presented sandwich structure.•Presenting coupled GDQM and NTIM to extract the dynamical responses of the nonlinear equations.•Presenting improved machine learning algorithm to measure nonlinear dynamics of the presented structure under complex situations. The measurement of the nonlinear dynamics of sandwich rotary sector plates is crucial for measurement engineers as it enables the precise analysis and understanding of the behavior of advanced composite structures under dynamic conditions. These measurements help in identifying and mitigating potential issues related to vibration, stability, and fatigue, which are critical in industries like aerospace, automotive, and civil engineering. Accurate data on nonlinear dynamics aids in the optimization of design, enhancing performance, durability, and safety. Furthermore, it supports the development of predictive maintenance strategies, reducing downtime and operational costs, and contributing to the advancement of engineering materials and techniques. So, in the current work, for the first time, nonlinear dynamics of sandwich rotary sector plate via a mathematical modeling and machine learning algorithm is presented. First, due to a lack of information on the nonlinear dynamics of sandwich rotary sector plates, a dataset for training, testing, and validating the machine learning algorithm is presented. For this purpose, using Hamilton’s principle, Von-Karman nonlinearity, and first-order shear deformation theory (FSDT), the nonlinear governing equations are obtained. Also, due to increasing stiffness and stability, an auxetic concrete foundation covers the sandwich structure. After that using the two-dimensional generalized differential quadrature method (GDQM) and Newmark’s time integration method (NTIM), the nonlinear equations are solved. This research provides valuable insights for engineers in designing advanced composite structures with improved dynamic properties. The results also contribute to the broader understanding of nonlinear dynamic interactions in complex material systems, paving the way for innovative applications in various engineering fields.