Abstract
Fractional derivative finite deformation theory and nonlinear finite element method were developed for evaluating dynamic characteristics of viscoelastic bodies used in shock and vibration reduction. Fractional differential orders from the static and dynamic testing of viscoelastic material with small strain were obtained. Then a fractional derivative constitutive model for finite deformation theory was constructed and nonlinear finite element equations of motion, involving a newly developed viscoelastic damping matrix as well as standard mass and stiffness matrices, were formulated. Based on this work, a nonlinear finite element computer program for the evaluation of vibration characteristics of viscoelastic products was developed. Simple numerical examples were computed and compared with the experimental results. Both results are in good agreement.
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