旋轉梁結構之振動分析

Abstract

本文的主要目的在探討旋轉梁的自然頻率。本文中考慮的梁係剛接在一以等角速度旋轉的圓柱上。本文利用非線性梁理論的一致線性化，虛功原理，d'Alembert原理在旋轉座標上上推導旋轉梁正確的線性運動方程式。本文中在分析時考慮了軸向變形及科氏力。本文中提出一套旋轉梁之自然頻率的級數解法。 本文最後以數值例題分析了不同轉速下，不同設定角，不同轉軸半徑及不同長度的梁之自然頻率，同時並探討了忽略科氏力對自然頻率的影響。

The major objective of this thesis is to investigate the nature frequency of rotating beam. The beam considered is rigidly tied to a rotating culinder with constant angular velocity. The exact linear equation of motion is derived by consistent linearization of the geoemtrically nonlinear beam theory, virtual work principle and d'Alembert principle at a rotating coordinates. The axial deformation and Coriolis force are considered in this paper. A method based on series solution is proposed to solve the nature frequency of rotating beam in this paper. Numericl examples are studied for the nature frequency of rotating beam with different angular velocity, setting angle, hub radius and length The influence of Coriolis force on nature frequency is also investigated.