Nonlinear Forced Vibration Analysis using ‘Elmer’ FEM Package to Develop Poincaré Map and Correlation Method-based Damage Indicators

Abstract

With the rapid advancement of sensor technology, structural health monitoring (SHM) is also blossoming with prowess in the field of civil, mechanical and aerospace engineering. It deals with the initiation of damage and its characteristic behavior in a deterministic or predictive way. The time-dependent fluctuation associated with the dynamic motion of structures was addressed with few efficient indicators in the past to identify the presence of damage as well as to localize the faulty area. The formulation of all those indicators is validated on specific structural arrangements with certain assumptions. This limitation is considered in this article to project the global applicability of the method along with the inherent constraints. The damage detection in the time-domain is considered to utilize direct accessibility of responses from the sensors attached to the members. It reduces the computational difficulty in transforming response to another domain and also associated approximations that emerge through numerical calculations. Broadly, two types of methods are discussed in this article along with modelling and analysis procedure; methods developed from cross-correlation of response and graphical method or Poincaré map. The model of cantilever beam and axial bar is developed in FreeCad where damage is induced by reducing either thickness or Young’s modulus of damaged elements to simulate cracked member. Meshing of member is done in Gmsh. To generate response history of state variables a newly developed finite element (FE) analysis software package Elmer is then employed for the dynamic analysis of the member with geometric nonlinearity. At last, application of Teager energy operator (TEO) in noise reduction is explained with a general example.