Nonlinear vibrations of elastic beams with external general visco-elastic devices

Vibration damping for slender beams is achieved by applying devices at external points. The latter consist of general single visco-elastic springpot elements. An approximate nonlinear boundary value problem is found in frequency domain that holds for moderately large vibrations or for linear beams with external nonlinear devices, both in the vicinity of primary resonances. The interaction force of a so-called springpot element is expressed as a sum of two separate forces: the first develops due to the external loading function at the device location, and the second contribution arises due to an imposed time-harmonic support excitation with no other external forces acting on the structure. Finally the nonlinear frequency response function follows from a (nonlinear) algebraic equation where the influence of the springpot element appears as isolated parameter