Forced vibration analysis of beams with frictional clamps

Abstract

This study investigates the vibration characteristics of rectangular cross-sectioned and straight beams with imperfect supports, focusing on the role of dry friction at the contact interfaces. The contact interactions are reduced to resultant point loads, and the friction at the contact interfaces is modelled using the Jenkins friction model, introducing nonlinearity into the system. These nonlinear terms are included in solution-dependent boundary conditions for the governing differential equation of beam vibration. Two cases are considered in detail and solved: one where the beam is tightened between rigid clamps at both ends and excited from the middle with a harmonic displacement function, and another where only one end is clamped with the other end free but excited with an imposed harmonic displacement. The governing differential equation is solved analytically, separating the motion into two distinct regimes - full-stick and full-slip, using the Galerkin method. The results acquired from this analytical model are then compared to those from a numerical model, which is built and solved using the finite element method combined with a frequency sweep and time-marching.