This paper presents a systematic and rigorous analysis on the convergence rates of the Harmonic balance Method (HB) for general smooth and non-smooth systems. In doing so, the convergence rates of Fourier truncation are established at first for functions with different smoothness, and then, the errors of HB are estimated with the help of a coercive condition and the established results on Fourier truncation errors. As is found in this work, when the restoring forces are discontinuous or of some special low smoothness, the convergence rates of HB become different from those of Fourier truncation. Numerical examples are studied and the results well verify the present theoretic convergence rates.

本文对一般光滑和非光滑系统的谐波平衡法（HB）的收敛速度进行了系统，严格的分析。为此，首先针对具有不同平滑度的函数建立傅立叶截断的收敛速度，然后借助强制条件估计HB的误差，并建立傅立叶截断误差的结果。从这项工作中可以发现，当恢复力不连续或具有某些特别低的平滑度时，HB的收敛速度将与傅里叶截断的收敛速度不同。数值例子进行了研究，结果很好地证明了目前的理论收敛速度。