Frequency response variability in friction-damped structures due to non-unique residual tractions: Obtaining conservative bounds using a nonlinear-mode-based approach

Abstract

Under static dry friction, the tangential friction force (residual traction) is non-unique within the Coulomb’s limits. The actual value of the residual traction depends on the load history and is generally unknown. This phenomenon can lead to a large variability of the vibration response if at least one but not all contacts are permanently sticking and there is coupling between tangential displacements and normal forces. In the present work, a method is developed that allows obtaining conservative upper and lower bounds of the frequency response. Focusing on primary resonances with well-separated modes, a Nonlinear-Mode-based approach is pursued. First, bounds of the nonlinear modal properties, specifically the amplitude-dependent modal frequency, damping ratio and deflection shape are computed. Then, interval arithmetic is applied to the closed-form expression governing the amplitude-frequency curves for a given harmonic excitation force. The method is numerically demonstrated for a planar structure coupled with two Jenkins-type contact elements. It is shown that for this system, the bounds of the modal properties can be simply obtained from the frictional limit cases (barely sticking contact), so that a potentially costly numerical optimization is not needed. It is concluded that the obtained frequency response bounds are indeed conservative but not overly conservative, and the method is computationally highly efficient as it relies on analytical developments. The developed method of Nonlinear-Mode-based forward propagation seems attractive also for other sources of uncertainty and experimentally identified bounds.