本文選題：譜元法　切入點(diǎn)：剛架　出處：《哈爾濱工業(yè)大學(xué)》2011年碩士論文

【摘要】：有限元法,有限差分法和譜元法是當(dāng)前被用來求解結(jié)構(gòu)動(dòng)力學(xué)問題的主要方法。其中譜元法因其采用與頻率有關(guān)的插值函數(shù)、與有限元方法相結(jié)合、對(duì)復(fù)雜邊界具有廣泛的適應(yīng)性以及具有譜方法的快速收斂性,具有重要的研究?jī)r(jià)值。 譜元法由有限元法、動(dòng)力學(xué)剛度法和譜分析方法的關(guān)鍵要素整合而來。精確的動(dòng)力學(xué)剛度矩陣以由控制方程的波動(dòng)解推導(dǎo)出的頻域上精確的動(dòng)力學(xué)形函數(shù)為基礎(chǔ),所以在理論上譜元法會(huì)得到精確的頻域解。本文在總結(jié)了譜元法的優(yōu)缺點(diǎn)之后,推導(dǎo)了桿單元和梁?jiǎn)卧膭?dòng)力學(xué)剛度矩陣,并計(jì)算了桿結(jié)構(gòu)和梁結(jié)構(gòu)的固有頻率和時(shí)域響應(yīng)。 然后,論文將譜元法應(yīng)用于桿系結(jié)構(gòu)的動(dòng)力學(xué)響應(yīng)分析和計(jì)算中。桿系結(jié)構(gòu)由于連接方式的不同被分為剛架結(jié)構(gòu)和桁架結(jié)構(gòu)。針對(duì)剛架結(jié)構(gòu)組裝了整體動(dòng)力學(xué)剛度陣,給出了整體結(jié)構(gòu)的運(yùn)動(dòng)方程,計(jì)算了結(jié)構(gòu)的固有頻率和時(shí)域響應(yīng),并與采用有限元方法得到的結(jié)果進(jìn)行了對(duì)比。從結(jié)果中可以看出譜元法在數(shù)值模擬中的獨(dú)特優(yōu)勢(shì)。 分別以含理想鉸的連接桿結(jié)構(gòu)和桁架結(jié)構(gòu)為對(duì)象,采用譜元法研究了鉸結(jié)構(gòu)對(duì)整體結(jié)構(gòu)動(dòng)力學(xué)行為的影響。論文將鉸模擬為分段線性模型,并將譜元法推廣應(yīng)用到求解分段線性問題,拓展了譜元法的應(yīng)用領(lǐng)域。在頻域下將鉸結(jié)構(gòu)考慮為一個(gè)譜單元,將鉸結(jié)構(gòu)和其它結(jié)構(gòu)的動(dòng)力學(xué)剛度矩陣整合起來得到整體結(jié)構(gòu)的動(dòng)力學(xué)剛度陣,進(jìn)而得到整體結(jié)構(gòu)的運(yùn)動(dòng)方程,通過求解整體結(jié)構(gòu)的動(dòng)力學(xué)方程,獲得結(jié)構(gòu)的時(shí)間響應(yīng)歷程曲線,分析了含鉸的連接桿結(jié)構(gòu)和桁架結(jié)構(gòu)動(dòng)力學(xué)行為。
[Abstract]:Finite element method, finite difference method and spectral element method are the main methods used to solve structural dynamics problems.The spectral element method has extensive adaptability to complex boundary and fast convergence of spectral method because of its use of frequency-related interpolation function and finite element method.The spectral element method integrates the key elements of finite element method, dynamic stiffness method and spectral analysis method.The exact dynamic stiffness matrix is based on the exact dynamic form function in the frequency domain derived from the wave solution of the governing equation, so the spectral element method can obtain the exact frequency domain solution in theory.After summarizing the merits and demerits of the spectral element method, the dynamic stiffness matrix of the bar element and the beam element is derived, and the natural frequency and the time domain response of the rod structure and the beam structure are calculated.Then, the spectral element method is applied to the dynamic response analysis and calculation of the bar structure.The bar structure is divided into rigid frame structure and truss structure because of the different connection mode.The integral dynamic stiffness matrix is assembled for the rigid frame structure, the motion equation of the whole structure is given, the natural frequency and the time domain response of the structure are calculated, and the results obtained by the finite element method are compared with those obtained by the finite element method.From the results, we can see the unique advantages of spectral element method in numerical simulation.The influence of the hinge structure on the dynamic behavior of the whole structure is studied by using the spectral element method, taking the connecting bar structure and the truss structure with ideal hinges as the objects.In this paper, the hinge is simulated as a piecewise linear model, and the spectral element method is extended to solve the piecewise linear problem, which extends the application field of the spectral element method.Considering the hinge structure as a spectral element in frequency domain, the dynamic stiffness matrix of the whole structure is obtained by integrating the dynamic stiffness matrix of the hinge structure and other structures, and then the motion equation of the whole structure is obtained.By solving the dynamic equation of the whole structure, the time response history curve of the structure is obtained, and the dynamic behavior of the connecting bar structure and truss structure with hinge is analyzed.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2011
【分類號(hào)】：TH113

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 張昊強(qiáng);豎向脈沖型地震下超高層建筑結(jié)構(gòu)的波動(dòng)分析[D];大連理工大學(xué);2013年

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本文編號(hào)：1716794