On Stress‐Driven Nonlocal Integral Model with Discontinuity for Modeling Torsional Vibration of Cracked AFG Miniaturized Rods With General Constraints

ABSTRACT In this work, we present a size‐dependent study of the dynamics of axially functionally graded (AFG) rods with general constraints. General boundary conditions (GBCs) are modeled by setting elastic spring constraints with torsional stiffness at both ends of the rod, while the gradient variation of the rod characteristic parameters along the axial direction is described by a power‐law model. The existence of cracks divides the beam into two parts connected by a rotational spring. In this case, by adopting the equivalently differential formulation derived from the stress‐driven nonlocal integral theory—which is rigorously complemented by a complete set of constitutive boundary and continuity conditions—a mathematically well‐posed model of the problem is established. All the variables in the formula of the differential problem are discretized, and the numerical solutions of the vibration frequencies of various bounded AFG rods are then established using the generalized orthogonal differential method (GDQM). After verifying the current formulas and results, the influence of various parameters, such as non‐local scale parameters, FG index, elastic boundary constraint strength, and crack‐related parameters, on the torsional frequency/formation of the structure is investigated in detail. It is expected that the outcomes are beneficial to the health monitoring and safety design of miniaturized components for micro/nano‐technological applications.