Energy dissipation formulas for boundary control of elastic structures: A higher-order Green’s identity approach

Authors

Toufik Ennouari

Abstract

                This paper presents explicit formulas for the energy dissipation rate in boundary control of elastic structures using higher-order Green’s identities in a port-Hamiltonian framework. A unified expression is derived for systems of order 2                    m                    that generalizes known results for Timoshenko beams and Kirchhoff plates. This formula facilitates passivity verification and leads directly to optimal linear-quadratic boundary feedback laws in the form of viscous damping. The analysis is extended to non-collocated boundary control and establishes generalized passivity conditions. Numerical simulations validate the exponential stability achieved with the proposed control laws and illustrate the trade-offs between damping strength and control effort.                  

Citation

• Journal: Journal of Vibration and Control
• Year: 2026
• Volume:
• Issue:
• Pages:
• Publisher: SAGE Publications
• DOI: 10.1177/10775463261450861

BibTeX

@article{Ennouari_2026,
  title={{Energy dissipation formulas for boundary control of elastic structures: A higher-order Green’s identity approach}},
  ISSN={1741-2986},
  DOI={10.1177/10775463261450861},
  journal={Journal of Vibration and Control},
  publisher={SAGE Publications},
  author={Ennouari, Toufik},
  year={2026}
}

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