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We prove that the von K´ arm´ an model for vibrating beams can be obtained as a singular limit of a modified Mindlin- Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth-order dispersive operator is added. We also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k, when suitable damping terms are added. As k ! ¥, one deduces the uniform exponential decay of the energy of the von K´´ model.

Asymptotics and stabilization for dynamic models of nonlinear beams