On the damped vibratory response of curved viscoelastic beams

An analysis is given of the damped forced vibratory response of viscoelastic beams with small initial curvature in order to explore the interaction of initial curvature with both extensional and shear deformation, as they provide energy dissipation mechanisms for the damped response. A non-dimensional variational statement is developed which governs the problem of the forced vibratory response of slightly curved Timoshenko beams including in-plane deformation, and appropriate parameters are defined. In particular, initial rise and shear parameters are seen to play important roles in the results.Numerical results are presented for the first three modes for both simple and clamped support conditions. In general, even a slight amount of initial curvature has a significant effect in decreasing the damped response for the first mode, and the actual effect is influenced strongly by the shear parameter. Initial curvature has a smaller influence on the higher modes. An understanding of when extensional or shear energy dissipation is dominant for certain ranges of values of the curvature and shear parameters is obtained by actual plots involving the appropriate form of energy dissipation. In general, extensional energy dissipation tends to dominate in the first mode for both support conditions, although the clamped beam tends to favor shear dissipation over a certain range of parameter values. The dominance of the shear mechanism, however, increases markedly for the higher modes for both support conditions.