We propose a reformulation for a recent integral equations approach to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation results in additional speed-up and better convergence. We show that the solutions of the reformulated equations are in one-to-one correspondence with those of the original integral equations and derive conditions under which a collocation-type approximation converges to the exact solution in the reformulated setting. Furthermore, we observe that model reduction using a selected set of vibration modes of the linearized system substantially enhances the computational performance. Finally, we discuss an open-source implementation of this approach and demonstrate the gains in computational performance using three examples that also include nonlinear finite-element models.

中文翻译：

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用于快速计算非线性周期响应的积分方程和模型简化

我们建议重新制定最近的积分方程方法，用于周期性受迫非线性机械系统的稳态响应计算。这种重新制定导致额外的加速和更好的收敛。我们表明，重构方程的解与原始积分方程的解一一对应，并导出了搭配型近似收敛到重构设置中精确解的条件。此外，我们观察到使用线性化系统的一组选定振动模式的模型简化大大提高了计算性能。最后，我们讨论了这种方法的开源实现，并使用三个还包括非线性有限元模型的示例展示了计算性能的收益。