DYNAMIC MODELING AND SIMULATION OF A HUB-FGM MICRO-BEAM BASED ON MESHLESS METHOD

This paper presents a comprehensive investigation into the dynamic characteristics of rotating functionally graded material (FGM) micro-beams, employing the meshless point interpolation method (PIM) and radial point interpolation method (RPIM) to describe the deformation field of flexible micro-beams. Based on the modified couple stress theory and the rigid-flexible coupled dynamic theory, the deformation displacement is formulated in a floating coordinate system. To ensure high accuracy in the dynamic model, the longitudinal shortening caused by transverse bending deformation which is called nonlinear coupling terms are taken into account, and all high-order terms that have been overlooked in existing research are retained in the formulation of the system’s kinetic energy. Concurrently, the potential energy expression is enhanced by including the couple stress tensor and curvature tensor, which are fundamental to accounting for size effects predicted by the modified couple stress theory. Utilizing the Lagrange’s equation of the second kind, the high-order rigid-flexible coupled (HOC) dynamic model of a rotating FGM micro-beam is systematically derived. Through a series of numerical simulations, the applicability and limitations of the first-order approximation coupled (FOAC) dynamic model are compared against those of the proposed HOC dynamic model, thereby validating the accuracy and necessity of the established comprehensive model. The factors affecting the dynamic characteristics and natural frequencies of FGM micro-beam such as the functionally gradient index, size-dependency and rotation law are discussed. When the thickness of the beam is reduced to approach the characteristic length parameters of the material, size effect on the dynamic characteristics and natural frequencies of FGM micro-beam cannot be ignored. The simulation results of the meshless method are compared with the traditional finite element method (FEM) and the assumed mode method (AMM). It is shown that the meshless method as a discrete method can be extended in the study of rigid-flexible coupled multi-body system dynamics, which enriches the discrete methods in the field of flexible multi-body system dynamics.