A strategy improving stiffness to resist local vibration of sandwich plates by extended Legendre higher-order model

Sandwich structures have been increasingly used in aerospace engineering, while local vibration modes of sandwich plates might occur earlier than global vibration modes attributing to the weak stiffness of the core layer, and it is difficult to predict such vibration modes. Therefore, local vibration modes are often discarded in the process of structural design, so that potential dangers might be encountered when the frequency of external load is close to the natural frequency of local vibration. To avoid such an issue, an extended Legendre higher-order theory (ELHT) is developed to accurately forecast the local dynamic behaviors of sandwich plates for the first time. Subsequently, an effective multi-objective optimization platform will be constructed to optimize the distribution of graphene-nanoplatelets (GPLs) in the core layer, so that natural frequencies of local vibration modes will be improved and largely more than the fundamental frequency. The B-spline basis functions are employed to describe various GPLs distributions, which is more convenient to produce original data for the machine learning method in the optimization process. Then, extreme gradient boosting optimized by Sparrow Search Algorithm (SSA-XGBoost) is utilized as the high-fidelity surrogate model to construct the objective functions to accelerate the interaction of the ELHT and non-dominated sorting sparrow search algorithm (NSSSA). By optimizing for minimum global and local fundamental frequency ratio and total mass of GPLs reinforced sandwich plates, the Pareto-optimal solutions are obtained from the present algorithm which can give an alternative suggestion for the future designer to ensure the structural dynamic safety of thick sandwich plates.