透過監控結構振動訊號以識別出機械、航太、及土木系統中是否存在破壞為相當重要的研究問題。當結構具有裂紋時，其斷面處會展現出間歇性開闔之非線性動態現象，因此無法使用線性振動的方法進行分析及監測。為了了解具裂紋結構的複雜非線性動態行為，本研究透過創新的數值方法以及實驗方法分析一具有斷裂面懸臂樑的非線性振動現象，並討論斷裂面參數對於振動特性的影響。
首先，本研究利用一離散元素方法(discrete element method)對一具有裂紋的懸臂樑進行建模，並使用雙線性剛性(bilinear stiffness)描述結構於斷裂面的間歇性開闔現象 ， 接著應用一近期開發的混成 解析數值 (hybrid symbolic numeric computational)方法估算懸臂樑於受到簡諧激振時的動態響應。我們最後透過實驗工作驗證數值分析的準確性。本研究發現具有裂紋的懸臂樑會展現出頻率偏移、次諧波共振(subharmonic resonance)、及渾沌(chaotic motion)等非線性現象，且上述現象可作為結構受到破壞時的識別特徵。本文最後提出一透過掃頻進行破壞識別的策略，並提出未來研究方向。

Structural damage occurs in a variety of civil, mechanical, and aerospace engineering systems, and it is critical to effectively identify such damage in order to prevent catastrophic failures. When cracks are present in a structure, the breathing phenomenon that occurs between crack surfaces typically triggers nonlinearity in the
dynamic response. In this work, in order to thoroughly understand the nonlinear effect of cracks on structural dynamics, both numerical and experimental analyses are conducted to investigate the crack-induced nonlinear dynamics of cantilever beams. First, a modeling method referred to as the discrete element (DE) method is employed to construct a model of a cracked beam. The DE model is able to characterize the breathing phenomenon of cracks. Next, a simulation technique referred to as the hybrid symbolic numeric computational (HSNC) method is used to analyze the nonlinear response of the cracked beam. The HSNC method provides an efficient way to evaluate both stationary and non-stationary dynamics of cracked systems since it combines efficient linear techniques with an optimization tool to capture the system’s nonlinear response. The proposed computational platform thus enables efficient multiparametric analysis of cracked structures. The effects of crack location, crack depth, and excitation frequency on the cantilever beam are parametrically investigated using the proposed method. Nonlinear features such as sub-harmonic resonance, non-stationary motion, multistability, and frequency shift are also discussed. Finally, an experimental analysis is conducted to validate the numerical results. The results of this work suggest that the potential cracks in cantilever beams can be identified using a frequency-sweep process.

摘要... I
Abstract...II
Acknowledgment...III
Vita... IV
Publications... IV
Content...V
List of figures... VI
List of tables... XI
Nomenclature...XII
Chapter 1 Introduction ...1
Chapter 2 Methodology...4
2.1 Construction of the discrete model...4
2.2 Numerical analysis of the nonlinear dynamics...7
2.3 Experimental setup ...10
Chapter 3 Results and Discussion...16
3.1 Numerical convergence analysis...16
3.2 Parametric analysis...23
3.3 Experimental results...33
3.4 Discussion...42
Chapter 4 Conclusions and Future Work...45
Reference ...47
Appendix...50

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