Coupling effects with vibration-based estimation of individual bolt tension in multi-bolt structures

Recent work with various single-bolt experimental setups has shown promising results for applying a vibration-based bolt tension estimation procedure. To estimate tension, the novel procedure models a bolt’s transverse vibrations with a single Euler–Bernoulli beam. The present work investigates the applicability of that novel approach when a structure contains more than one bolt. The principal question is if the vibrational response obtained from excitation of a specific bolt, mounted in a structure with other similar bolts, can still roughly be modelled as an independent single-bolt system, or if the other bolts affect the vibrational response in an undesirable way. To determine if the novel single-bolt approach is applicable, it is necessary to gain insight into possible coupling phenomena. For this, a two-bolt problem is investigated, modelled both as a coupled two-beam Euler–Bernoulli model and numerically with FEM software, and with experimental testing of two real bolts mounted in the same structure. It is found that strongly coupled bending vibrations, with in-and out-of-phase modes, only occur when tension and boundary stiffness in the two bolts are very close to identical. When the bolts have different boundary parameters, the coupling is weak, and the two bolts can roughly be treated as two independent single-bolt systems. In both situations, it is actually possible to estimate bolt tension and boundary stiffness based on measured transverse natural frequencies using a single-bolt beam model.