Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/154549
Title: A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics
Authors: Li, Li
Lin, Rongming
Ng, Teng Yong
Keywords: Engineering::Mechanical engineering
Issue Date: 2020
Source: Li, L., Lin, R. & Ng, T. Y. (2020). A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics. Applied Mathematical Modelling, 84, 116-136. https://dx.doi.org/10.1016/j.apm.2020.03.048
Journal: Applied Mathematical Modelling
Abstract: To overcome the long wavelength and time limits of classical elastic theory, this paper presents a fractional nonlocal time-space viscoelasticity theory to incorporate the non-locality of both time and spatial location. The stress (strain) at a reference point and a specified time is assumed to depend on the past time history and the stress (strain) of all the points in the reference domain through nonlocal kernel operators. Based on an assumption of weak non-locality, the fractional Taylor expansion series is used to derive a fractional nonlocal time-space model. A fractional nonlocal Kevin–Voigt model is considered as the simplest fractional nonlocal time-space model and chosen to be applied for structural dynamics. The correlation between the intrinsic length and time parameters is discussed. The effective viscoelastic modulus is derived and, based on which, the tension and vibration of rods and the bending, buckling and vibration of beams are studied. Furthermore, in the context of Hamilton's principle, the governing equation and the boundary condition are derived for longitudinal dynamics of the rod in a more rigorous manner. It is found that when the external excitation frequency and the wavenumber interact with the intrinsic microstructures of materials and the intrinsic time parameter, the nonlocal space-time effect will become substantial, and therefore the viscoelastic structures are sensitive to both microstructures and time.
URI: https://hdl.handle.net/10356/154549
ISSN: 0307-904X
DOI: 10.1016/j.apm.2020.03.048
Rights: © 2020 Elsevier Inc. All rights reserved
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:MAE Journal Articles

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