Predicting S4 Beam Joint Nonlinearity Using Quasi-Static Modal Analysis

Abstract

Recently, a new algorithm was presented (Festjens et al., Int J Mech Sci 75 (2013) 170–177) that allows one to predict the effective natural frequency and damping ratio as a function of amplitude for a structure with bolted joints. This paper applies a variant on that algorithm to a finite element model of the “S4 Beam” (two C-shaped beams bolted together on their ends) and compares the results with the measurements described in (Singh et al., IMAC 2019). The algorithm, which is here referred to as Quasi-Static Modal Analysis (QSMA), is applied to a detailed finite element model of the beam in the commercial software package, Abaqus®. Coulomb friction is assumed to govern the contact interface. Amplitude dependent damping and natural frequency curves are calculated for the structure and compared to experimental measurement. Several studies are included which explore the solver tolerances and preload values needed to reach agreement with experimental measurements. Additionally, the shape of the actual contact interfaces is measured using a profilometer and fed into the model to quantify the effect of slight curvature in the contact.