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Statistical random response analysis and reliability design of structure system with non-linearity

機譯：非線性結構系統(tǒng)的統(tǒng)計隨機響應分析與可靠性設計

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In this paper, a method to analyse a complex non-linear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process for the statistical analysis. When modelling the overall non-linear system, the overall system is divided into substructures and these are approximately transformed into modal coordinates with the random excitation. The modal equations of the overall system are expanded sequentially according to the non-linear order. Then, the perturbed equations are synthesised into the overall system and solved in a probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with the non-linear stochastic problem. The obtained statistical properties of the non-linear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.
機譯：提出了一種分析隨機激勵下的復雜非線性結構系統(tǒng)的方法。首先，將實際的隨機激勵（例如地震）近似于相應的高斯過程進行統(tǒng)計分析。在對整個非線性系統(tǒng)進行建模時，會將整個系統(tǒng)劃分為子結構，并通過隨機激勵將它們近似轉換為模態(tài)坐標。整個系統(tǒng)的模態(tài)方程根據(jù)非線性順序依次展開。然后，將擾動方程綜合到整個系統(tǒng)中，并以概率方式求解。根據(jù)非線性隨機問題，回顧了隨機振動應用中感興趣的隨機過程的幾種統(tǒng)計特性。在每個子結構中評估獲得的非線性隨機振動的統(tǒng)計特性。與數(shù)值模擬結果進行比較，證明了該方法的有效性。

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