本文選題：小波有限元 + 懸臂裂紋梁�。� 參考：《華中科技大學(xué)》2011年碩士論文

【摘要】：結(jié)構(gòu)裂紋的出現(xiàn)和在交變應(yīng)力作用下的不斷擴(kuò)展,容易造成結(jié)構(gòu)的破壞進(jìn)而導(dǎo)致重大安全事故的發(fā)生,因此在早期對裂紋進(jìn)行定量識別以保證結(jié)構(gòu)安全在工程實(shí)際中具有重要意義。振動診斷法因其方便、快速的特點(diǎn)在工程故障診斷中應(yīng)用廣泛,小波有限元因其多分辨率分析的特性在處理裂紋等奇異性問題上精度較高,因此本文研究基于小波有限元的懸臂裂紋梁參數(shù)辨識問題。 首先,計(jì)算了Daubechies小波尺度函數(shù)和聯(lián)系系數(shù),推導(dǎo)并計(jì)算了Coiflet小波尺度函數(shù)和聯(lián)系系數(shù),將小波多分辨分析的特性通過尺度函數(shù)作為插值函數(shù)引入有限元,構(gòu)造了Daubechies小波梁單元和Coiflet小波梁單元,并通過算例驗(yàn)證了小波梁單元在梁彎曲問題和振動問題中具有很高精度。 然后,將裂紋視為無質(zhì)量扭轉(zhuǎn)線彈簧,建立懸臂裂紋梁的小波有限元模型,求解不同裂紋參數(shù)下懸臂梁的前三階固有頻率,與解析解吻合程度很高,驗(yàn)證了懸臂裂紋梁小波有限元模型在裂紋辨識正問題中的有效性;采用等高線法,將實(shí)測固有頻率作為裂紋辨識反問題的輸入,利用實(shí)測固有頻率等高線投影線的交點(diǎn)進(jìn)行裂紋深度和位置的識別,通過文獻(xiàn)中給出的實(shí)測固有頻率成功進(jìn)行了裂紋辨識,驗(yàn)證了懸臂裂紋梁小波有限元模型在裂紋辨識反問題中的有效性。 最后,進(jìn)行了懸臂裂紋梁激振實(shí)驗(yàn),利用實(shí)驗(yàn)測得的固有頻率進(jìn)行基于小波有限元模型的懸臂裂紋梁參數(shù)辨識,取得了很好的效果。
[Abstract]:The appearance of structural cracks and the continuous expansion under the action of alternating stress can easily lead to the destruction of the structure and lead to the occurrence of major safety accidents. Therefore, quantitative identification of cracks in early stage to ensure structural safety is of great significance in engineering practice. Vibration diagnosis method is widely used in engineering fault diagnosis because of its convenience and rapidity. Wavelet finite element method has high accuracy in dealing with singularity problems such as cracks because of its multi-resolution analysis. So the parameter identification of cantilever crack beam based on wavelet finite element method is studied in this paper. Firstly, the scaling function and the contact coefficient of Daubechies wavelet are calculated, and the scaling function and contact coefficient of Coiflet wavelet are deduced and calculated. The characteristics of wavelet multi-resolution analysis are introduced into finite element method by scaling function as interpolation function. The Daubechies wavelet beam element and the Coiflet wavelet beam element are constructed, and the results show that the wavelet beam element has a high accuracy in the bending and vibration problems of the beam. Then, the crack is regarded as a massless torsion line spring, and the wavelet finite element model of the cantilever crack beam is established. The first three natural frequencies of the cantilever beam with different crack parameters are solved, which is in good agreement with the analytical solution. The validity of the wavelet finite element model of cantilever crack beam in the positive problem of crack identification is verified, and the measured natural frequency is used as the input of the inverse problem of crack identification by using the contour method. The crack depth and position are identified by using the intersection point of the measured natural frequency contour projection line, and the crack identification is successfully carried out through the measured natural frequency given in the literature. The validity of the wavelet finite element model of cantilever crack beam in the inverse problem of crack identification is verified. Finally, the vibration experiment of cantilever cracked beam is carried out, and the parameter identification of cantilever crack beam based on wavelet finite element model is carried out by using the natural frequency measured in the experiment, and good results are obtained.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2011
【分類號】：TH165.3

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 余博;基于零矩尺度函數(shù)有限元的轉(zhuǎn)軸裂紋識別方法與應(yīng)用[D];華中科技大學(xué);2012年

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本文編號：1952272