Abstract
Beam-like structures are the most common components in real engineering, while single side damage is often encountered. In this study, a numerical analysis of single side damage in a free-free beam is analysed with three different finite element models; namely solid, shell and beam models for demonstrating their performance in simulating real structures. Similar to experiment, damage is introduced into one side of the beam, and natural frequencies are extracted from the simulations and compared with experimental and analytical results. Mode shapes are also analysed with modal assurance criterion. The results from simulations reveal a good performance of the three models in extracting natural frequencies, and solid model performs better than shell while shell model performs better than beam model under intact state. For damaged states, the natural frequencies captured from solid model show more sensitivity to damage severity than shell model and shell model performs similar to the beam model in distinguishing damage. The main contribution of this paper is to perform a comparison between three finite element models and experimental data as well as analytical solutions. The finite element results show a relatively well performance.
Highlights
Structural health monitoring (SHM) has been a research focus in the past decades since more and more structures are sophisticated with the development of science and technology
One can find that from analytical solution, solid model, shell model to beam model, the errors of each mode increase, which confirms that analytical solution considers the beam-like structure to be continuous elastic system, and finite element models discrete the structure and approximate the results
This can be explained by Equation (3), each natural frequency is corresponding to the mode shape; (ii). generally, the natural frequencies change much more than the modal assurance criterion (MAC) value, this suggests that the natural frequency is more sensitive than MAC of mode shapes
Summary
Structural health monitoring (SHM) has been a research focus in the past decades since more and more structures are sophisticated with the development of science and technology. Due to the high cost of experiment in real engineering structures, numerical analysis has been exploited as another useful but affordable tool in SHM, and many other directions. Even lots of research work have been conducted on beam-like structures, difficulty in detecting the damage still emerges, and double side saw cut in beam has been more often studied. 2. Theoretical background Considering an elastic system, for example, a loaded beam, the dynamic equilibrium equation of damped vibration can be expressed as (1). As to modal analysis determining the dynamic characteristics of the systems, damping and external loading forces are assumed to be zero in order to achieve a simplest harmonically vibrating model. Modal assurance criterion (MAC) is frequently used; for mode shape before and after damage, it can be expressed as doi:10.1088/1742-6596/628/1/012036. Where φiu represents the ith mode shape under intact state, φid means the ith mode shape under damaged state
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