Efficient Reduced-Order Modeling and Response Approximation for Cracked Structures Available to Purchase

Analysis of the influence of cracks on the dynamics of structures is critical for design, failure prognosis, and structural health monitoring. Predicting the dynamics of complex cracked structures is computationally challenging for two reasons: (1) the model size is generally large, and (2) the piecewise-linear nonlinearity caused by contact eliminates the use of linear analysis tools. Recently, a technique referred to as X-X_r approach was developed to efficiently reduce the model size of cracked structures. The method employs relative coordinates to describe the motion of crack surfaces such that an effective model reduction can be achieved using Craig-Bampton component mode synthesis. More recently, a method referred to as the generalized bilinear amplitude approximation (generalized BAA) was developed to approximate the amplitude and frequency of piecewise-linear nonlinear systems. This paper modifies the generalized BAA method and combines it with the X-X_r approach to efficiently predict the dynamics of complex cracked structures. The combined method is able to estimate the amplitude and frequency of cracked systems with a reduced computational effort. The proposed approach is demonstrated on a three degree of freedom spring-mass system and a cracked cantilever beam.