預載重剪力變形拱之動力及挫屈行為研究

Abstract

首先，本研究的控制方程乃是一受預載重而引至含有初始應力場之彈性體，且考慮剪力變形之拱，透過變分原理所推得的。本研究主要結合動態勁度法與級數解，探討考慮剪力變形及預載重之平面定斷面圓拱與變曲率拱之面內自由振動及挫屈行為。利用增加切割元素個數或靜態內力項之泰勒展開項數及動態位移函數之級數解項數，均可得到精確解，且不會有數值上之困難。 本研究中探討圓心角及厚勁比對圓拱無因次化頻率與挫屈載重之影響；接著再探討展開角、細長比及b/a對橢圓拱無因次化頻率與挫屈載重之影響。另外，本文亦探討不考慮剪力變形對無因次化頻率及挫屈載重之影響。

The first known governing equations for vibrations preloaded, shear deformable arches and derived according to a variational principle for dynamic problems of an elastic body with initial stresses. The study is combined with dynamic stiffness matrixes and series solution, investigate the in-plane free vibration and buckling behaviors of loaded circular and variable curvature arches with considering shear deformation. Convergent results are obtained by increasing the number of elements or by increasing both numbers for Taylor’s expansion series terms and series solution terms, can’t encounter the convergence problem of the solution. The study investigate the opening angle and thickness-to-radius ratio influence on nondimensional frequencies and buckling loads of circular arches. Moreover the study also investigate the opening angle, slenderness-to-length ratio and b/a influence on nondimensional frequencies and buckling loads of elliptic arches. Furthermore, the study also investigate the effects with no shear deformation for nondimensional frequencies and buckling loads.