Coulomb sliders are used widely in order to model frictional interfaces. In many applications, the nonlinear Frequency Response Functions (FRFs) of these systems is desired, but it is extremely computationally expensive to use time-domain integration methods to compute the steady-state response. The nonlinear force and stiffness of these devices depends on the position of sliders, and the implicit nature of the slider positions makes these systems hysteretic and therefore non-trivial to address using conventional continuation methods. This paper proposes a novel numerical method, dubbed ”Hysteresis Identification via Reversal Points or (HIRP)” that can compute the steady-state harmonically forced response of frictional nonlinear systems. For this purpose, a quasi-static algorithm is introduced which can evaluate the state of sliders at any time based on the reversal points over a period. This reduces the number of state variables needed in the continuation routine by at least an order of magnitude. The method has been tested by computing the harmonic response of a hysteretic system with multiple Coulomb sliders. The method is evaluated on multi-degree of freedom systems with Iwan joints, demonstrating that the method can be a valuable tool for predicting the nonlinear, steady-state response of hysteretic systems.

库仑滑块被广泛用于模拟摩擦界面。在许多应用中，需要这些系统的非线性频率响应函数 (FRF)，但使用时域积分方法来计算稳态响应在计算上非常昂贵。这些设备的非线性力和刚度取决于滑块的位置，而滑块位置的隐含性质使这些系统具有滞后性，因此使用传统的连续方法来解决并不容易。本文提出了一种新的数值方法，称为“通过反转点或（HIRP）的滞后识别”，可以计算摩擦非线性系统的稳态谐波受迫响应。以此目的，引入了一种准静态算法，该算法可以根据一段时间内的反转点随时评估滑块的状态。这将延续例程中所需的状态变量的数量减少了至少一个数量级。该方法已通过计算具有多个库仑滑块的迟滞系统的谐波响应进行了测试。该方法在具有 Iwan 关节的多自由度系统上进行了评估，表明该方法可以成为预测滞后系统的非线性稳态响应的宝贵工具。