Efficient optimization of clutched inerter dampers using mixed Lagrangian formalism
File(s)
Published version
Author(s)
Zhang, Yixuan
Lavan, Oren
Málaga-Chuquitaype, Christian
Type
Journal Article
Abstract
Clutched Inerter Dampers integrate inerters with one-way clutches and dampers, enabling the inerters to disengage from the host structure and dissipate energy, suppressing undesirable energy feedback and avoiding the direct alteration of the structural period, making clutched inerter dampers particularly attractive for vibration mitigation and energy harvesting applications. However, the nonlinearity and discontinuity introduced by clutch engagement-disengagement mechanisms pose significant challenges for their accurate numerical modelling and optimization-based design. Existing optimization approaches for such systems are predominantly based on simplified or linearised numerical models, or on exhaustive parameter scanning, which either fail to capture the true nonlinear behaviour or become impractical for realistic design spaces.
We present an adjoint-based, gradient-driven optimization framework for structures equipped with clutched inerter dampers in which the Mixed Lagrangian Formalism is employed as the time-integration scheme. Within the proposed framework, the nonlinear behaviour of clutched inerter dampers is fully captured, while computational efficiency and numerical robustness are achieved through the Mixed Lagrangian Formalism, which reduces the cost of individual response-history analyses and enhances stability in the presence of non-smooth dynamics. In addition, adjoint-based sensitivity analysis significantly decreases the number of simulations required during the optimization process. The framework enables efficient optimization of design parameters as demonstrated through a series of representative case studies. Our results show that, despite strong nonlinearity and discontinuous system responses, analytical gradients can be consistently derived, leading to substantial reductions in computational cost and improved optimization efficiency.
While the actual performance may be influenced by the characteristics of the design landscape and the choice of initial conditions, the proposed framework provides a robust and extensible basis for further methodological developments. It can be readily extended in future work to accommodate alternative optimization strategies or enhanced formulations.
We present an adjoint-based, gradient-driven optimization framework for structures equipped with clutched inerter dampers in which the Mixed Lagrangian Formalism is employed as the time-integration scheme. Within the proposed framework, the nonlinear behaviour of clutched inerter dampers is fully captured, while computational efficiency and numerical robustness are achieved through the Mixed Lagrangian Formalism, which reduces the cost of individual response-history analyses and enhances stability in the presence of non-smooth dynamics. In addition, adjoint-based sensitivity analysis significantly decreases the number of simulations required during the optimization process. The framework enables efficient optimization of design parameters as demonstrated through a series of representative case studies. Our results show that, despite strong nonlinearity and discontinuous system responses, analytical gradients can be consistently derived, leading to substantial reductions in computational cost and improved optimization efficiency.
While the actual performance may be influenced by the characteristics of the design landscape and the choice of initial conditions, the proposed framework provides a robust and extensible basis for further methodological developments. It can be readily extended in future work to accommodate alternative optimization strategies or enhanced formulations.
Date Issued
2026-02-01
Date Acceptance
2026-01-19
Citation
Computers & structures, 2026, 322
ISSN
0045-7949
Publisher
Elsevier
Journal / Book Title
Computers & structures
Volume
322
Copyright Statement
© 2026 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
License URL
Identifier
10.1016/j.compstruc.2026.108121
Publication Status
Published
Article Number
108121
Date Publish Online
2026-01-27