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等效周期和有效阻尼比的合理取值是保证等效线性化方法求解精度的关键。该研究利用在自振周期和阻尼比两维空间中的全局优化搜索手段,提出了一种确定等效线性化方法系统参数的标准粒子群优化算法。算例分析验证了优化算法求解的可行性。在保证系统参数合理取值的同时,标准粒子群优化算法的计算效率约为统计分析方法的2.0%,从而克服了统计分析方法在确定等效周期和有效阻尼比时计算量庞大的缺点。该文最后应用所提出的标准粒子群优化算法,以弹塑性非线性单自由度体系为具体的研究对象,分析并推导了等延性系数假定下其等效线性化方法系统参数的计算公式。
The reasonable value of equivalent period and effective damping ratio is the key to ensure the accuracy of equivalent linearization method. In this paper, a global optimization search method is proposed in the two-dimensional space of natural vibration period and damping ratio, and a standard particle swarm optimization algorithm for determining the system parameters of the equivalent linearization method is proposed. The case study verifies the feasibility of the optimization algorithm. While ensuring the reasonable value of the system parameters, the computational efficiency of the standard Particle Swarm Optimization algorithm is about 2.0% of the statistical analysis method, thus overcoming the shortcomings of the statistical analysis method in calculating the equivalent period and the effective damping ratio. Finally, by applying the standard Particle Swarm Optimization (PSO) algorithm proposed in this paper to the elasto-plastic nonlinear single-degree-of-freedom system, the calculation formula of its equivalent linearization method under the assumption of equal ductility coefficient is analyzed and deduced.