Project supported by the National Natural Science Foundation of China(Nos.11972129 and12372008);the National Major Science and Technology Projects of China(No.2017-IV-0008-0045);the Natural Science Foundation of Heilongjiang Province of China(No.YQ2022A008);the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2023006);the Polish National Science Centre of Poland under the OPUS 18 grant(No.2019/35/B/ST8/00980);the Tianjin University Independent Innovation Foundation of China(No.2023XJS-0038)。
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a...