Fast computation of steady-state response for high-degree-of-freedom nonlinear systems
Fast computation of steady-state response for high-degree-of-freedom nonlinear systems
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DOI：
10.1007/s11071-019-04971-1
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发表时间：
2019-07-01
影响因子：
5.6
通讯作者：
Haller, George
中科院分区：
文献类型：
--
作者：
Jain, Shobhit;Breunung, Thomas;Haller, George
我们讨论了一种积分方程的方法，使快速计算的非线性多自由度的机械系统下的周期性和准周期性的外部激励的响应。这个积分方程的核心是一个绿色的功能，我们明确计算一般的机械系统。我们推导条件下，积分方程可以解决一个简单而快速的皮卡德迭代，即使是非光滑的机械系统。这种迭代的收敛性不能保证近共振强迫，我们采用牛顿-拉夫森迭代代替，获得鲁棒收敛。我们进一步表明，这种积分方程的方法可以附加标准的延续计划，以实现额外的，显着的性能提高，超过常见的方法来计算稳态响应。
We discuss an integral equation approach that enables fast computation of the response of nonlinear multi-degree-of-freedom mechanical systems under periodic and quasi-periodic external excitation. The kernel of this integral equation is a Green's function that we compute explicitly for general mechanical systems. We derive conditions under which the integral equation can be solved by a simple and fast Picard iteration even for non-smooth mechanical systems. The convergence of this iteration cannot be guaranteed for near-resonant forcing, for which we employ a Newton- Raphson iteration instead, obtaining robust convergence. We further show that this integral equation approach can be appended with standard continuation schemes to achieve an additional, significant performance increase over common approaches to computing steady-state response.