一阶线性微分方程 meaning in English

linear first-order differential equation

Are uncertain and should be regarded as random variables , therefore the reinforced concrete frame is stochastic structure inherently , and then its motive equations converted to combined random differential equations for the uncertain parameters and external random excitation . these equations were solved by order - orthogonal expansion method with pseudo - excitation method , and then the statistic stochastic responses of random structure were obtained . at last , based on the stochastic cumulative damage model with double parameters developed by park , formulas were formulated for calculating structural earthquake damage probability using the structural reliability theory ( mainly jc algorithm ) in extensive random space
首先对受地震激励的剪切型钢筋混凝土结构进行建模，用随机等效线性化方法将二阶非线性微分方程组化成一阶线性微分方程组(或称之为状态方程) ；再考虑材料等参数的随机性，则状态方程成为复合随机微分方程组，将扩阶系统方法和虚拟激励方法推广并应用于这个复合随机微分方程组，求出结构的随机响应量的统计参数；最后采用随机累积损伤破坏准则，在广义随机空间内，用jc算法求解失效概率，进而求出结构的抗震可靠度。