請用此 Handle URI 來引用此文件: http://hdl.handle.net/11455/91413
標題: Vibration Analysis of Beamlike Frames Consisting of Fiber-Reinforced Composite Rods of Circular Cross Sections
圓形截面複合材料桿所組成似樑之剛架的振動分析
作者: 陳昱瑜
Yu-Yu Chen
關鍵字: Composite;Beamlike Frame;Vibration Analysis
複合材料;樑形剛架;振動分析
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摘要: The objective of this thesis is to develop a finite element computer program for analyses of natural frequencies, mode shapes, as well as transient responses of beamlike composite frames using MATLAB. The beamlike frames are made up of fiber-reinforced composite rods of circular cross section. The mathematical model of rods has included the effects of axial, lateral and transverse displacements, shear deformation of cross sections, and torsion deformation. In the computer program, first, one chooses the desired geometry profiles of the beamlike frames and the material properties of the rods. Next, the mass and stiffness matrices of the aforementioned straight rod finite element and the coordinate transformation matrix associated with each rod are computed. In the end, the global mass and stiffness matrices of beamlike frames are established. By using the program developed in this thesis, first, the natural frequencies and mode shapes of isotropic steel beamlike frames are analyzed and compared with those of ANSYS. Their differences in natural frequencies are shown to be about 3 to 6 %. Next, under the condition that the frames have the same geometry profile and dimensions of rods, the beamlike frames made up of composite rods that are symmetric laminated as [0/45/-45/0]s, anti-symmetric laminated as [(45/-45)3], and quasi-isotropic laminated as [90/45/0/-45], as well as of isotropic steel rods are analyzed. The natural frequencies and mode shapes of these frames with one of its edge fixed are investigated. For planar as well as spatial beamlike frames being analyzed, considering the first eight natural frequencies, the natural frequencies of the case with symmetric laminated composite rods are all larger than those of the corresponding modes of three other cases. The case of quasi-isotropic is the second, anti-symmetric case is the third, while the natural frequencies of the case with isotropic steel rods are the lowest. But there are exceptions. For planar beamlike frames, the natural frequencies of the third and the fifth mode (both are torsion modes) of the case of anti-symmetric are little bit higher than those of quasi-isotropic case. Finally, the transient responses of both planar and spatial beamlike frames made up of above four cases of rods are analyzed. Two approaches, the direct integration method and the modal superposition method, are used to obtain the transient responses. The results obtained by both methods are shown in good agreement. The results also indicate that although the natural frequencies of the frame with isotropic steel rods are lower than the other three composite cases, its largest transient displacement is the smallest among the four. The probable cause for this is that the density of steel is much larger than that of the composite material being considered. For the three other composite cases, because they all use the same composite material, the order of their largest transient displacements is in reverse order of the magnitudes of their natural frequencies.
本論文主要目的在於建立一個可以分析複合材料樑形剛架自然頻率、模態以及暫態響應的有限元素Matlab程式。所分析的樑形剛架是以圓形截面的複合材料直桿所組成,其中桿件具有軸向、橫向與側向位移、橫向與側向剪力變形、扭轉變形等效應。於程式中首先選定想要分析剛架的幾何外形及各桿件的材料特性。其次,經由計算得出上述直桿之元素之質量與勁度矩陣與各桿件的座標轉換矩陣,最後建立複材樑形剛架的全域質量及勁度矩陣。 本文利用上述有限元素程式,分析等向性鋼材樑形剛架並與ANSYS所分析之結果比較,兩者之間的差異大約在3~6%。其次分析在相同的桿件尺寸和幾何外形的條件下,疊層角度分別為對稱疊層[0/45/-45/0]s、反對稱疊層[(45/-45)3]和類等向性疊層[90/45/0/-45]的複合材料桿件,以及等向性鋼材桿件所建立的樑形剛架,探討當其一端固定時之自然頻率及模態的變化。對所分析的平面和空間樑形剛架而言,前八個自然頻率以採用對稱疊層複材桿最大,其次為類等向性疊層複材桿,接著為反對稱疊層複材桿,而採用等向性鋼材桿則最小。但其中的例外是平面樑形剛架的第三和第五模態(兩者皆為扭轉模態)的自然頻率值,當採用反對稱疊層複材桿時會稍高於使用類等向性疊層複材桿。 本文中最後分別利用直接積分及模態疊加兩種方法,分析平面與空間樑形剛架的暫態響應,並探討等向性鋼材桿件和不同疊層角度的複合材料桿件,所組成的樑形剛架的暫態響應。結果顯示上述兩種方法所求得的暫態響應還蠻一致。其次,雖然採用等向性鋼材桿時,剛架的自然頻率在四個例子中最低,但其最大的暫態位移響應值相對上卻最小,究其原因應該是等向性鋼材的密度遠大於所採用複合材料密度的關係。其餘三個複材例子,由於是使用同一種複材,它們最大暫態位移響應的大小順序,則與其自然頻率大小順序相反。
URI: http://hdl.handle.net/11455/91413
文章公開時間: 2017-08-31
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