论文标题
非线性周期响应的快速计算的积分方程和模型降低
Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response
论文作者
论文摘要
我们提出了Ja那教，Breunung \＆Haller [Nonlinear dyn。 97，313--341（2019）]，用于定期强迫非线性机械系统的稳态响应计算。这种重新构造导致额外的加速和更好的收敛性。我们表明，重新计算方程的解决方案与原始积分方程的对应关系是一对一的，并得出了搭配类型近似在重新安装环境中收敛到精确解决方案的条件。此外，我们观察到使用线性化系统的选定振动模式的模型降低显着提高了计算性能。最后，我们讨论了这种方法的开源实现，并使用包括非线性有限元模型的三个示例来证明计算性能的增长。
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] 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.
