Abstract
AbstractWe 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.
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