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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/38146


    Title: 彎曲且預扭曲桿件受彈性支撐之動態行為
    Other Titles: On the Dynamics of Curved and Pretwisted Rods Subjected to Elastic Restraints
    Authors: 蔡慧駿;葉豐輝
    Contributors: 淡江大學機械與機電工程學系
    Keywords: 動態響應;模態;邊界條件;細長比;自然頻率;Dynamic Response;Mode Shape;Boundary Condition;Slenderness;Natural Frequency
    Date: 1996-12-14
    Issue Date: 2010-01-11 14:45:36 (UTC+8)
    Abstract: 本文研究空間中彎曲且預扭曲桿件的運動方程組及邊界條件,並探討細長比、彎曲曲率、扭轉曲率、斷面形狀、錐度及彈性支等變化對桿件自然振動頻率與模態之影響。研究中以中心線位移與斷面旋轉量為參數,推導出彎曲且預扭曲桿件受彈性支的動能、位能及彈簧能函數;再採用漢彌爾頓定理(Hamiltom's Principle)由此兩參數推導得運動方程組與彈性支之邊界條件。應用此運動方程組將可分析幾何參數及彈性支等變化對彎曲且預扭曲桿件動態行為的影響。分析中採用Rayleigh-Ritz法藉由滿足直桿邊界之多項式函數以推導出彎曲且預扭曲桿件的動態反應特徵方程組。應用此特徵方程組將可解析彎曲且預扭曲桿件的自然振動頻率及模態。研究中先由方形斷面曲桿動態反應中探討細長比、彎曲曲率及扭轉曲率之影響,接而藉由矩形斷面曲桿探討斷面寬高比、錐度及彈性支之影響特性。經此研究,可發現細長比、彎曲曲率、扭轉曲率、斷面寬高比、錐度及彈性支等變化對彎曲且預扭曲桿件之動態行為均有顯著之影響。
    This study formulates the equations of motion and presents the dynamic response for a curved and pretwisted rod with elastic restraints. The effects of slenderness, curvature, torsion, cross section shape, taper, and elastic restraints on natural frequencies and mode shapes of the rod are discussed. Expressions for the kinetic, potential, and elastic restraint energy functions of a curved and twisted rod subject to elastic restraints is derived using Kingsbury's assumptions of centerline displacements and cross section rotations. These expressions are first used to drive the equations of motion and boundary conditions using Hamilton's Principe. The equations of motion are then specialized for various variations of centerline curvature, torsion, cross section shape, and taper along the rod axis. Next, the kinetic potential, and elastic restraint energy functions are used to formulate Rayleigh-Ritz solutions for the mode shapes and natural frequencies of a curved and pretwisted rod with elastic restraints. Effects of slenderness, curvature, torsion, cross section shape, taper, and elastic restraints on the dynamic response for a curved and pretwisted rod are then thoughtfully studied .
    Relation: 中華民國力學學會第二十屆全國力學會議論文集(二)=Proceedings of the 20th National Conference on Theoretical and Applied Mechanics (II),頁17-24
    Appears in Collections:[機械與機電工程學系暨研究所] 會議論文

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