具等向性彎曲剛度但無自發扭曲之長細螺旋杆的彈性性質

淡江大學機構典藏 > 理學院 > 物理學系暨研究所 > 學位論文 > Item 987654321/32501

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题名:	具等向性彎曲剛度但無自發扭曲之長細螺旋杆的彈性性質
其它题名:	Elasticity of a helical filament with isotropic bending rigidity and free of spontaneous torsion
作者:	詹政諱;Jan, Jeng-huei
贡献者:	淡江大學物理學系碩士班周子聰;Zhou, Zicong
关键词:	螺旋;長杆;彈性;Elastic rod;Helix
日期:	2006
上传时间:	2010-01-11 02:14:50 (UTC+8)
摘要:	我們利用歐拉角推導出了一根橫切面為圓形，但是無自發扭曲的均勻彈性杆之形狀方程式。我們證明了兩端閉合的細杆通常存在著平面形曲線形的解。我們探討了在外力與外力矩下，形成螺旋杆的邊界條件暨實驗條件。我們發現要形成螺旋形，Euler角必須為常數並由自然曲率所決定。我們研究了螺旋杆在外力和外力矩下的彈性性質。我們嚴格證明了當力矩為零時，在改變外力時螺旋杆的伸長不會有突然跳躍的現象。這行為與一根有自發扭曲的均勻彈性杆之行為相當不同，並解釋了為何在巨觀力學實驗中難以觀察到這種跳躍。然而在非零值的固定外力矩下，改變外力則螺旋的伸長可能會有一次突然的轉變。 We derive the shape equations in terms of Euler angles for a uniform elastic filament with circular cross section but free of spontaneous torsion. We show that in general there are planar curve solutions for a closed rod. We study the boundary conditions (i.e., experimental conditions in a force experiment) to form a helical filament under external force and twisting. We find that to form a helix, the Euler angle must be a constant determined by the spontaneous curvatures. We study the elasticity of a helical filament under different conditions. We find that the extension of a helix under fixed and finite torque may subject to a one-step sharp transition with increasing stretching force. However, we show exactly that there is not jump of extension for a helical filament free of external torque. This behavior is quite different from a uniform elastic rod with circular cross section and spontaneous torsion, and provides another very important reason why one cannot observe the sharp jump of extension for most macroscopic helical springs.
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