The safety and integrity of engineered structures are critically dependent on maintaining sufficient preload in their bolted joints. This preload can be dynamically lost due to sustained vibrations or sudden shock that are large enough to induce slip in the threads. While high-fidelity finite element simulations and analytical methods can accurately model the loss of preload for a single bolt, their prohibitive computational expense and complexity render them unfeasible for analyzing large-scale structures with many bolts. This creates a critical need for reduced-order models that capture the essential physics of loosening while remaining computationally efficient. This paper introduces a reduced-order modeling methodology for predicting the loosening of bolted lap joints subjected to transverse shock excitation. The core idea is to treat the bolt tension as a dynamic degree-of-freedom that governs the effective properties of the joint through tension-dependent stiffness and damping that couple the components together. The methodology is applied to a pair of oscillators coupled by a lap joint with a strain-sensing bolt. Three different sets of experimental measurements are used to interrogate the dynamics of the system. Mathematical models are identified for the joint stiffness and damping and the instantaneous tension, which are combined with the equations of motion for the oscillators to simulate and reproduce the experimental measurements. Ultimately, the results validate the treatment of bolt tension as a dynamic degree-of-freedom, such that the methodology provides an effective framework for predicting loosening behavior in bolted joints.
He et al. (Sun,) studied this question.