Adaptability and Comparison of the Wavelet-based with Traditional Equivalent Linearization Method and Potential Application for Damage Detection
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Date
2003-02-23
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Abstract
The main objective of this research work is to compare a wavelet transform based Equivalent linearization technique, presented herein with the traditional Equivalent linearization method. In addition, the application of this wavelet-base method to the damage detection of a single Degree of Freedom system has also been presented.
In many practical applications the system of concern is nonlinear. In general, and especially in random vibration analysis, it is difficult to obtain a closed form solution for dynamic response of a nonlinear system. Therefore, it is necessary to replace the nonlinear system with an equivalent linear system. Method of equivalent linearization has been extensively used in these engineering applications. The wavelet analysis allows us to capture temporal variations in the energy and frequency content. In combining the wavelet analysis technique and the well-known Equivalent linearization method, a nonlinear system can be approximated as a time dependent linear system. By comparing the information of the time-varying natural frequency coefficient between the healthy system and the damaged system, the introduced damage can be identified at a particular time.
The first part of this document consists of a detailed description of some of the most common types of time-frequency methods that have been developed or used for vibration and frequency analysis over the last several decades. The fundamentals of the traditional
Equivalent Linearization Method have been introduced to demonstrate the general procedure to linearize a system. An important linearization method, utilizing Wavelet based transformation is then presented.
In this study, the benefits of this proposed method have been verified by its application in a typical nonlinear system. Different wavelets and different excitations are used in performing this analysis. To verify the accuracy of the wavelet based method, the traditional Equivalent Linearization results of displacement have been compared with those obtained by this method. In order to check the feasibility of the methodology, the relationship of the restoring force vs. displacement has been compared between the original nonlinear system and the equivalent linear system. For further application in the structural health monitoring, this method has been applied to some simple cases to see the effect of damage detection. To simplify the entire procedure of derivation, some formulation work introduced by Basu, Gupta [1997] and Roberts and Spanos [1990] have been followed.
Results from this study demonstrate that this approach is more accurate for non-stationary excitation compared with the traditional Equivalent Linearization method. It is also suitable for damage detection even when the introduced damage is fairly small.
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Keywords
Equivalent Linearization, Wavelet Analysis
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Degree
MS
Discipline
Mechanical Engineering
