本計畫將利用柴比雪夫配置法分析非均勻軸向功能梯度提摩辛格樑的撓曲振動。樑的斷面及材料性 質假設沿樑長度方向呈變化。該非均勻軸向功能梯度樑之微分特徵值方程式，係使用柴比雪夫微分 矩陣將其離散成矩陣特徵值方程式。為驗證所提出分析模型的準確性，分析結果將與文獻上已發表 的相關數據進行比較。接著探討不同錐度係數、梯度係數及邊界條件對非均勻軸向功能梯度樑系統 自然頻率的影響效應。咸信本計畫的分析模型可幫助研究者經由對非均勻軸向功能梯度樑振動表現 的參數分析，以更加了解各種幾何及材料參數對功能梯度樑結構振動的影響。
The present proposal will analyze the bending vibration of non-uniform axially functionally graded Timoshenko beams based on Chebyshev collocation method. The cross-sectional and material properties of the beam are assumed to vary continuously along the beam length. The Chebyshev differentiation matrices will be used to reduce the ordinary differential equations into a set of algebraic equations to form the eigenvalue problem associated with the free vibration. To validate the accuracy of the proposed model, the calculated results will be compared with those in the published literature. Then, the effects of the taper ratio, volume fraction index, and restraint types on the natural frequency of axially functionally graded beams with non-uniform cross section will be examined. It is believed that the proposed model is valuable for the parametric studies to understand better the various geometric and material parameters of the functionally graded beam affecting its vibration characteristics.
