رویکرد ترکیبی FEM–ANN برای تحلیل و تشخیص چندجرمی در نانورزونانسورهای گرافنی

Graphene’s remarkable stiffness, extremely low density, and large surface-to-mass ratio make it highly responsive to minute mass variations, even down to the zeptogram scale. Although most prior studies have concentrated on single-particle adsorption, practical scenarios often involve multiple particles randomly distributed on the surface, leading to complex nonlinear vibration behaviors. In this work, a hybrid FEM–ANN framework is developed that integrates high-fidelity finite element simulations with a deep-learning neural network to analyze the vibrational response of graphene sheets under multi-mass loading. The dataset generated from simulations—incorporating variations in aspect ratio, sheet dimensions, number of particles, and their random distribution—is used to train and validate the neural network. The trained model accurately predicts nonlinear frequency shifts with substantially reduced computational cost compared to full numerical simulations. This hybrid approach provides a reliable and efficient tool for rapid multi-mass detection in graphene nano resonators, with potential applications in biosensing and environmental monitoring.