Eventos Anais de eventos
MECSOL 2022
8th International Symposium on Solid Mechanics
The arc-length method utilized for nonlinear frequency response: an improved radius control
Submission Author:
Lucas Tanabe , SP
Co-Authors:
Lucas Tanabe, Alberto Luiz Serpa
Presenter: Lucas Tanabe
doi://10.26678/ABCM.MECSOL2022.MSL22-0198
Abstract
One of the most difficult challenges of computational structural mechanics is solving nonlinear problems. This is the reason why several methods have been developed over the last few decades to deal with these more complex mathematical models. Most of these approaches are based on the Newton-Raphson method. However, some of the nonlinear problems present inflection points, resulting in difficult paths in the load/displacement space, which such algorithms fail to determine precisely. The arc-length method is capable of solving problems with limit points, which is a common occurrence in snap-back and snap-through phenomena. This method imposes an additional constraint to the system of nonlinear equations of a given problem to favor convergence and overcome the limit points. One of the challenges of the method is the radius control of the additional constraint. It represents a key factor for the algorithm to be successful and efficient, therefore different approaches have been studied over the years. Although the arc-length method has been mainly used to determine load/displacement paths, it can also be used to determine frequency response functions (FRFs). This study aims to determine nonlinear FRFs using the arc-length method and propose modifications to the radius control in order to increase performance. Initially, the traditional arc-length algorithm is used to determine FRFs with classic nonlinearities such as cubic stiffness and gap nonlinearity. Later the proposed modifications to the radius control are introduced. The changes proved to be relevant, since the number of solution points to correctly determine the FRF is greatly reduced, increasing computing efficiency.
Keywords
nonlinearity, Arc-length method;, Frequency Response Functions, nonlinear vibration
