Mathias Legrand (McGill University)

Title:

Modal Analysis of One Dimensional Structures Prone to Unilateral Contact Conditions

Abstract:

The prediction of resonance in vibrating structures is a subject of importance in the field of mechanical engineering and is useful for structural health as well as for estimating the capabilities of vibrating structures. While classical modal analysis for linear systems relies on eigenvalue analysis, nonlinear dynamical systems lack superposition and the notion of modes of vibration has been extended to the concept of nonlinear normal modes which are seen as one-parameter continuous families of periodic motions of the investigated system. It is known that nonlinear normal modes feature energy-dependent natural frequencies. The presentation will focus on a subclass of mechanical systems where the nonlinearity stems from unilateral contact and frictional occurrences. Formulation, solution methods and solutions will be presented on a one-dimensional bar example.