Estimating bolt tightness from measured vibrations: Effective linearity of nonlinear boundary stiffness

Experimental evidence shows that the tightness of a bolt can be estimated from its vibrational response using a pre-stressed beam model with linear stiffness at its boundaries. We show how considering only linear boundary stiffness successfully reproduce the experimental results. A model of multiple nonlinear springs, modelling the asperities, is presented and it is shown that as the number of asperities increases the system’s response becomes linear-like.