This work proposes a new calculation algorithm of the Wentzel–Kramers–Brillouin (WKB) solution for slow linear time-varying (LTV) systems based on the recursive formulation. For a linear dynamic system with time-varying (TV) mass, damping or stiffness, the recursive relations in real function form among the components of the WKB solution are obtained. The integral terms within the sampling intervals that cannot be solved analytically are approximated by simple algebraic calculations with high precision. Thus, the conventional expression of the WKB solution involving complex numerical integral terms is reduced to an analytical recursive formulation. An explicit function relationship between the TV system parameters and the dynamic response can be obtained when the external excitation is given. In the premise of similar accuracy, the recursive formulation has much higher efficiency than the conventional calculation process, which is verified by applying the proposed method to a particular LTV dynamic system.

这项工作提出了一种新的Wentzel-Kramers-Brillouin（WKB）解决方案的计算算法，该算法基于递归公式，用于慢线性时变（LTV）系统。对于具有时变（TV）质量，阻尼或刚度的线性动力系统，获得了WKB解的各组成部分之间的实函数形式的递归关系。采样间隔内无法解析求解的积分项可以通过简单的代数计算以高精度进行近似。因此，涉及复杂数值积分项的WKB解决方案的常规表达式简化为解析递归公式。当给出外部激励时，可以获得电视系统参数与动态响应之间的明确函数关系。在精度类似的前提下，