Buckling Load Estimation for Sandwich Plates with Innovative Circular Cell Cores via Nondestructive Vibration Correlation Technique and Machine Learning

The vibration correlation technique (VCT) has emerged as an advanced and nondestructive approach for structural buckling analysis, offering substantial potential for high-level engineering applications. This study aims to estimate the buckling load of a sandwich plate with a novel circular cell core using VCT. The sandwich plate is designed based on a unit cell characterized by three adjustable parameters. Machine learning algorithms (MLAs) are initially employed to model the relationship between these design parameters (inputs) and key performance indicators (outputs), namely, the specific buckling load to weight ratio (p0/m=pc) and the first specific natural frequency to weight ratio (f0/m=fc). The resulting predictive models are integrated into a genetic algorithm (GA) as an objective function to maximize both (pc) and (fc) simultaneously, enabling the identification of optimal design parameters. Subsequently, a homogenization method is applied to determine the equivalent mechanical properties of the circular cell core. The structural behavior is further analyzed using first-order shear deformation theory, with buckling and free vibration equations solved through a meshless numerical method. The VCT is then implemented to estimate the buckling load, and its predictions are validated against experimental results. Among the three VCT variants, the third method demonstrates superior accuracy, achieving a prediction error of less than 6.2%, thereby proving its efficiency over alternative approaches. This integrated framework highlights the synergy of machine learning, optimization algorithms, and advanced structural theories in achieving robust and efficient structural designs.