| 摘要: | 本計畫將利用柴比雪夫配置法分析雙向功能梯度提摩辛格樑的振動表現。樑的材料性質假設同時沿樑長度及厚度方向呈變化。雙向功能梯度樑之微分特徵值方程式，將使用柴比雪夫微分矩陣將其離散成矩陣特徵值方程式，據以進行自由振動分析。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。接著探討不同細長比、材料分布型態、梯度係數及邊界條件對雙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雙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雙向功能梯度樑結構振動的影響。
The present proposal will study the vibration behaviors of bi-directional functionally graded Timoshenko beams based on Chebyshev collocation method. The material properties of the beam are assumed to vary simultaneously across the beam length and thickness. 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 obtained by other investigators. Then, the effects of the slenderness ratio, material distribution types, gradient index, and restraint types on the natural frequency of bi-directional functionally graded beams 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 bi-directional functionally graded beam affecting its vibration characteristics. |
