Generalized Kelvin–Voigt Damping for Geometrically Nonlinear Beams

Strain-rate-based damping is investigated in the strong form of intrinsic equations three-dimensional geometrically exact beams. Kelvin–Voigt damping, often limited literature to linear or two-dimensional beam models, generalized case, including rigid-body motions. The result an elegant infinite-dimensional description beams that facilitates theoretical analysis and sets baseline for any chosen numerical implementation. In particular, dissipation rates equilibrium points system are derived most general case one which a first-order approximation resulting terms taken. Finally, examples given validate model against nonlinear damped Euler–Bernoulli (where detail on how equivalent using our formulation obtained) support analytical results energy decay solutions caused by damping. Throughout paper, relevance higher-order terms, arising from description, accurate prediction its effect dynamics highly flexible structures highlighted.