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標題: 超大型多孔媒體有限元素結構動態模擬
Dynamic Simulation of Huge Porous Medium Structures by the Finite Element Method
作者: 康清志
Kang, Ching-Jyh
關鍵字: dynamic;porous medium;finite element
出版社: 機械工程學系
全身性振動(whole body vibration)已經被證實對於人體脊椎和關節具有
, 因此暸解脊椎運動骨節的自然振頻變得十分重要. 過去在此領域上的研
究, 多因所用的數
學模式的不健全以及體外實驗的簡化, 使得人們對脊椎振動方面的知識仍
相當缺乏. 以一套
高效率且合理的計算方法, 於高速電腦上模擬體內力學行為將是十分可貴.
本研究以多孔媒體有限元素法為基礎, 每個元素節點上同時具有三個固體
液體平移自由度, 用以模擬脊椎運動骨節於體內(in vivo) 的力學行為.
脊椎骨節之有限元素模式時所耗費的時間相當多, 研究中利用一套演繹法
種不同坐姿下, 脊椎的三維六面體多孔彈性有限元素模式. 因所模擬的結
構物, 如人體脊椎
通常包含數千個自由度, 所以其自然振動頻率亦有數千個, 研究中利用次
演繹法針對四種不同人體脊椎姿態; (1)脊椎於打直, 無曲率的狀態;
姿態; (3)脊椎於高背墊的姿態; (4)脊椎於低背墊的姿態; 將其所形成的
應的小矩陣, 再以Q.R 疊代法分別求取其特徵值, 可有效得到結構最低數
個振動頻率, 藉以
判斷結構元素的自然震動模態, 以暸解其動態形式. 研究結果顯示, 十一
頻率約為2.0Hz 左右. 本研究除了作為暸解脊椎的自然振頻外, 對於具有
境的改善, 如卡車座椅, 飛機座椅等等, 在設計上亦有正面的參考價值.

Whole body vibration (WBV) has been proved that
it significantly contributes to injuries and fun
disorders of the skeleton and of joints including spine.
Thus, it is getting important to understand the natural
frequency of the spine motion segments. People knows
less about spine motion segment because of using the
distemperelly mathematical formula and the simplification
of in vitro experiments. It's pretty important for
in vivo simulation on a high speed supercomputer based
on the caculating way possesses both high efficiency
and reasonableness.
The study is based on the porous media finite
element method, each node contains three solid
translation degrees of freedom and three fluid
translation degrees of freedom in order to simulate the
behaviour of the human spine. It's time-consuming to
establish manually the finite element model of the spine.
The present study used superior alogorithm to establish
the spinal 3-dimensional poroelastic hexahedron finite
element models under all different sitting posture. The
imitating structure contains thousands of degrees of
freedom such as human spine, so it also has thousands
of natural vibration frequency. In the research we use
substructure theory and Lanczos alogrithm to four
different posture of human spine: (1)straighted spine
and the status of no curve ; (2) spine in normal
standing posture ; (3) lumbar pad on the high back
position ; (4) lumbar pad on the low back position; to
translate the small matrices with the same effect from
large matrices and then to get its eigenvalue separately
by the method of Q.R iteration. By such doing, we can
get several minimum vibration frequency in order to
judge the natural model shape of structural element and
to understand its model shape. The result of the
research reveals that the first vibration frequency of
the eleven sections is about 2.0 Hz. The research is
not only to understand the natural resonant frequency
of spine but also to offer the improvement of the
mechanical environment which has the vibration
frequency and so on . It also offers the affermative
referental value.
Appears in Collections:機械工程學系所

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