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对有间隙系统自激振动非线性方程的解析解进行了分析，通常平均法产生误差的重要原因在于假设平均法的解时未考虑间隙的影响，从而提出一种新的方法，即加权平均法。经验证，计算精度符合工程要求，为某些非线性方程提供了一条求其近似解析解的途径。
The analytical solution of the nonlinear equation with self-excited vibration of a clearance system is analyzed. The most common reason for the error in the averaging method is the assumption that the influence of the clearance is not taken into account when solving the averaging method, so a new method, weighted average method . It is verified that the calculation accuracy accords with the engineering requirements and provides a way for some nonlinear equations to find their approximate analytic solutions.