Adjoint sensitivities for the optimization of nonlinear structural dynamics via spectral submanifolds
Matteo Pozzi (Politecnico di Milano)
Jacopo Marconi (Politecnico di Milano)
Shobhit Jain (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Mingwu Li (Dalian University of Technology, Southern University of Science and Technology )
Francesco Braghin (Politecnico di Milano)
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Abstract
This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using spectral submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with respect to parameters up to arbitrary polynomial orders, enabling efficient and accurate optimization of the nonlinear frequency-amplitude relation. Sensitivity expressions are obtained via the adjoint method, which significantly reduces computational cost compared to direct differentiation as the number of parameters increases. A key feature of the framework is the automatic adjustment of the expansion order of SSM-based reduced-order models using user-defined error tolerances during optimization. We demonstrate the effectiveness of the approach through several numerical examples, including the first application of topology optimization in nonlinear structural dynamics via arbitrary-order SSMs. Hence, the proposed framework extends the applicability of SSM-based optimization to practical engineering problems, providing a robust tool for designing and optimizing nonlinear mechanical structures.
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