{'fraction_non_alphanumeric': 0.01095290251916758, 'fraction_numerical': 0.0, 'mean_word_length': 5.6231884057971016, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Fractional Derivative Viscoelastic Model for Hybrid Active-Passive Damping Treatments in Time Domain - Application to Sandwich Beams

This work presents a finite element formulation for the dynamic transient analysis of a damped adaptive sandwich beam composed of a viscoelastic core and elastic-piezoelectric laminated faces. The latter are modeled using the classical laminate theory, which takes the electromechanical coupling into account by modifying the stiffness of the piezoelectric layers. For the core, a fractional derivative model is used to characterize its viscoelastic behavior. Equations of motion are solved using a direct time integration method based on the Newmark scheme in conjunction with the Grunwald approximation of fractional derivatives. Emphasis is given to the finite element implementation of the fractional derivative model and to the influence of the electromechanical coupling.