A subspace expanding technique(SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom(MDOF) engineering systems by discretizing the space into smaller subdomains,...A subspace expanding technique(SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom(MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highlyefficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation,and optimization problems in complex MDOF nonlinear dynamic systems.展开更多
基金the National Natural Science Foundation of China (Nos. 11702213,11772243,11572215,and 11332008)the Natural Science Foundation of Shaanxi Province of China(No. 2018JQ1061)。
文摘A subspace expanding technique(SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom(MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highlyefficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation,and optimization problems in complex MDOF nonlinear dynamic systems.
