Free and forced vibration mitigation of nonlinear functionally graded beams based on higher order shear deformation theories using NES

This study investigates the effective mitigation of free and forced vibrations in nonlinear functionally graded (FG) shear deformable beams through the application of a nonlinear energy sink (NES) near resonance (1:1). FG structures, characterized by varying material properties across dimensions, pose unique challenges in vibration control. We employ a comprehensive approach, combining higher-order shear deformation theories with advanced numerical methods. Our investigation begins by modeling a geometrically nonlinear beam using von Kármán theory. The equations of motion are derived through the assumed modes method and the Lagrange approach. To analyze free vibrations, we calculate both linear and nonlinear frequencies using the assumed modes method and the local concordant deformation assumption (LCDA), respectively. Our research primarily focuses on the forced vibration analysis performed using the complexification-averaging method. Steady-state frequency response curves are systematically generated using an arc-length continuation method, revealing valuable insights into the system’s behavior under various conditions. An optimization procedure employs a genetic algorithm to fine-tune NES parameters, resulting in an impressive 92.5% reduction in vibration amplitude. Notably, our study critically evaluates different shear deformation theories and investigates how varying FG material distributions influence optimal NES parameters.