Review of Nonlocal-in-Time Damping Models in the Dynamics of Structures

In the present paper, the nonlocal-in-time damping models, called “damping-with-memory” models, are reviewed. Since such models do not involve the distribution along the longitudinal coordinate, they are easily adjustable for the FEM (Finite Element Model) algorithm, which is a big advantage due to...

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Bibliographic Details
Published in:Axioms 2023-07, Vol.12 (7), p.676
Main Authors: Sidorov, Vladimir, Shitikova, Marina, Badina, Elena, Detina, Elena
Format: Article
Language:English
Subjects:
Algorithms
Civil engineering
Composite beams
Composite materials
Computer simulation
Damping (Mechanics)
Deformation
Energy dissipation
Equations of motion
finite element analysis
Finite element method
Friction
Hypotheses
internal friction
Least squares method
Manufacturing
Mathematical analysis
Mathematical models
nonlocal damping
Strain rate
Structural dynamics
Vibration damping
Viscoelasticity
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Summary:In the present paper, the nonlocal-in-time damping models, called “damping-with-memory” models, are reviewed. Since such models do not involve the distribution along the longitudinal coordinate, they are easily adjustable for the FEM (Finite Element Model) algorithm, which is a big advantage due to the fact that FEM is the most-used method in engineering calculations. Within damping-with-memory models, the internal damping of a structure at the current time, is assumed to be dependent not only on the instant strain-rate magnitude or displacement-velocity magnitude but also on the strain-rate or velocity values along the previous time history. The greater the gap between the two time points, the lower the influence that one of them has on the other. To implement a composite beam vibration simulation involving damping with memory, the equation of motion of a structure written in the matrix form could be solved using the central difference method. The models constructed could be calibrated based on 3D numerical simulation data with the least squares method. It has been shown that the results obtained using the implementation of a calibrated damping-with-memory model within the 1D finite-element beam algorithm are in good correlation with those given by the 3D-FEM numerical simulation data.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12070676