本文主要在研究具隨機性質複合材料積層板之隨機振動，本研究包括積層板的自由振動分析及隨機響應分析。假設縱向彈性模數、橫向彈性模數、剪力模數及卜松比為隨機變數，而激振力為白噪音過程。文中導入一階剪變形理論，有限元素分析法及擾動法來計算積層板的統計特徵值，再利用Newmark演算法來計算積層板之共變異矩陣，據此求得積層板位移及速度的均方值。本文範例包含了三種層疊角度的積層板，結果顯示，特徵值之平均值及變異數與蒙地卡羅模擬值相當吻合，而縱向彈性模數的隨機擾動對積層板之特徵值、位移及速度之影響遠大於其它參數。

The main purpose of the thesis is to study the random vibration of laminated composite plates with random material properties. The free vibration analysis and the random response analysis are included in the present study. The material properties, such as longitudinal elastic modulus, transverse elastic modulus, shear modulus and Poisson’s ratio are considered as random variables, and the excitation is a white noise process. The first-order shear deformation theory, the finite element method, and the perturbation method are together employed to evaluate the statistical eigenvalues of laminated composite plate, then the Newmark algorithm is applied to calculate the covariance matrix of response. Accordingly, the variance of the eigenvalue and the mean square value of displacement and velocity of laminated composite plates are obtained. The illustrated examples include three different stacking sequences of laminated composite plates. The results show that the mean and variance of the eigenvalue are good agreement with those calculated by using the Monte Carlo simulation, and the random effects of longitudinal elastic modulus perturbated are more significant than other material parameters on the eigenvalue, displacement and velocity of laminated composite plate.

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