Nonlinear damping models for linear conservative mechanical systems with preserved eigenspaces: a port-Hamiltonian formulation

Thomas Hélie (1, 2) , Denis Matignon (3)

1 Analyse et synthèse sonores [Paris]
2 S3AM - Systèmes et Signaux Sonores : Audio/Acoustique, instruMents
3 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

This paper addresses the derivation of a class of phenomenological but physically-grounded linear and nonlinear damping models, which preserve the eigenspaces of conservative linear mechanical problems. After some recalls on the finite dimensional case and on the class of linear damping of Caughey type, an extension of this class to nonlinear models is introduced. These passive systems are recast in the port-Hamiltonian framework and generalized to the case of infinite dimensional systems. These results are applied to an Euler-Bernoulli beam, excited by a distributed force. Simulations are presented for nonlinear damping configurations. They can be used to provide sounds of wooden or metallic type (such as xylophone or glockenspiel) and some interpolated versions.

Mots clés: energy storage; port-Hamiltonian systems; eigenfunctions; damping; nonlinear model; partial differential equations; sound synthesis

Domaines: Sciences de l'ingénieur [physics]

Thomas Hélie, Denis Matignon. Nonlinear damping models for linear conservative mechanical systems with preserved eigenspaces: a port-Hamiltonian formulation. Lagrangian and Hamiltonian Methods for Non Linear Control, IFAC, Jul 2015, Lyon, France. ⟨hal-01231810⟩