A multiscale model for modal analysis of composite structures with bolted joints

A new finite element(FE) model considering surface roughness of contact interfaces in a bolted composite joint, consist of laminated composite beams and fasteners (i.e., bolt, nut and gasket) along with thin-layer interfaces, was developed to model the dynamic response of the bolted joint. The macro-properties of the thin-layer interfaces were derived through micro-analysis on the single-asperity contact in conjunction with fractal contact theory. Firstly, normal (i.e., storage normal modulus) and tangential contact stiffness (including both storage and loss tangential modulus) of a single-asperity contact was expressed with external loads and surface properties of the contact interface, according to Hertzian contact theory and Mindlin micro-slip model, respectively. Subsequently, the contact stiffness of the interfaces which feature a multi-asperity contact in the micro perspective, subject to different pressure, was derived by integrating the contact stiffness of single asperity in the contact region. The damping and the stiffness of the composite structures with bolted joints were modelled using frequency-dependent modulus using complex eigenvalue method that were implemented in ABAQUS FE code. Predicted damping ratio and resonant frequency of the bolted composite joint under different residual torques were examined by comparing with the experimental investigation. Results from theoretical prediction and experiment are in good consistency, which shows resonant frequency for a bolted joint decreases whereas damping ratio increases with a reduce in the residual torque applied on the bolt.