高阶单步法的非线性误差传递效应分析

Nonlinear error propagation effect of high order single step method

对拟动力试验方法中的高阶单步法进行了深入研究,分析了算法的误差传递效应。通过引入系统结构刚度变化系数,研究非线性系统下算法的稳定性及其阻尼特性,在此基础上分析了刚度变化系数及参数β对系统误差传递效应的影响,最后通过数值仿真实验对分析结果进行验证。高阶单步法对非线性系统具有良好的适应能力,能够有效控制系统结构刚度变化过程中累积误差,同时,适当调节β值可以进一步削弱非线性系统中的误差传递效应。

Here, the high order single step method for pseudodynamic tests was studied deeply and the error propagation effect of the method was analyzed. By introducing structural stiffness variation coefficients of a system, the stability and damping characteristics of the method for nonlinear systems were investigated. Then, the influences of stiffness variation coefficients and the parameter β on the system error propagation effect were analyzed. Finally, a numerical example was taken to verify our analysis results. It was shown that the high order single step method has a good adaptability for nonlinear systems and can effectively control the cumulative error when the structural stiffness of a system is changing, meanwhile, the error propagation effect in a nonlinear system can be further mitigated by appropriately adjusting the parameter β.