Competitive Time Marching Solution Methods for Systems with Friction-Induced Nonlinearities

Abstract

Finding efficient and accurate solution methods for nonlinear equilibrium equations is a challenging task. This is the case of systems with friction-induced nonlinearities, e.g., friction-damped turbomachinery assemblies and automotive applications such as brakes. In order to tackle this strategic task, several methods have been developed, both in the time and in the frequency domains. Time marching methods are regarded as the most accurate option, but their computational cost becomes prohibitive when friction nonlinearities are present. This poses a problem in all those cases where alternative frequency domain methods cannot be applied effectively, e.g., if transients, non-periodic excitation/solution, or highly nonlinear systems are of interest. The purpose of this paper is to propose three independent methods to make time-marching more competitive. Two of these methods can be applied to any existing direct integration scheme with minimal adjustments, but the computational time cut they introduce is significant. The last method is instead tailored for systems where the inertia force contribution is negligible. All methods are thoroughly validated numerically using a standard Newmark-
 
 
 β
 
 
 integration scheme as a reference.

Modal Derivatives for Efficient Vibration Prediction of Geometrically Nonlinear Structures with Friction Contact

“…The implicit Newmark method (average acceleration method) [34] with adaptive time stepping [35] is employed to obtain the time history of the transient response. In each time step, the second-order nonlinear Equation ( 3) is solved by the Newton-Raphson algorithm.…”