Abstract

A new approach is presented for the vibration of non-smooth structural systems with dry friction and unilateral contact. These nonlinearities are ubiquitous in engineering, and turbomachinery rotors are a prime example of industrial systems subject to a variety of intermittent contact and frictional occurrences. While non-smooth nonlinearities are commonly expressed as a complementarity system of equalities and inequalities, the key idea here is to formulate them as non-smooth equality-only conditions, which together with the equations of motion are then satisfied in a weak integral sense through a weighted residual formulation. The resulting algebraic nonlinear equations are solved numerically using an adapted trust region nonlinear solver and basic integral quadrature schemes. The approach is developed for one-dimensional friction, extended to two-dimensional friction and contact, and applied to the fir-tree blade attachment of a helicopter engine bladed disk. The method is shown to be compact, effective, and computationally efficient. Periodic solutions with intricate sticking, sliding and separation phases are found with a high degree of accuracy for large numbers of Fourier harmonics. Importantly, the equality-based formulation does not suffer from the typical limitations or hypotheses of existing frequency-time domain methods for non-smooth systems, such as regularization, penalization, or massless frictional interfaces.