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Gen-guo, LI; Zhu, Zhihui; Chang-jun, Cheng

doi:10.1023/a:1025662518415

Cited by 17 publications

(1 citation statement)

References 5 publications

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“…In other words, since to obtain an elastic solution, from which it is quite easy to pass to a viscoelastic solution, is only an intermediate goal (the final goal is to obtain a solution to the original problem of linear viscoelastic equations), then there are ways to achieve the final goal, bypassing the stage of constructing a sufficiently "good" elastic solution and using, at the same time, the advantages of the accumulated experience in solving continual scleronomic problems of elasticity, provided by the FEM and FDM in the form of software packages and integrated systems. In [11][12][13][14][15], a method is presented for determining the dynamic characteristics of a viscoelastic beam in the framework of the one-dimensional theory of viscoelasticity. The hereditary Boltzmann-Voltaire theory was used to describe dissipative processes in the building material.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

et al. 2021

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The article deals with forced vibrations of a high-rise axisymmetric structure, represented as a viscoelastic beam of an annular section with a variable slope of the generatrices and variable thickness. The research was conducted to analyze the behavior of a high-rise structure for various kinematic effects. The task is to determine the displacements of the points of a high-rise structure at different time points under different kinematic effects. The methods were developed and a computer program was built; forced vibrations of high-rise axisymmetric structures under various kinematic actions, considering viscoelastic properties of the material, were investigated in linear, nonlinear, and viscoelastic formulations. The study of the dynamic behavior of a high-rise structure, taking into account the nonlinear and dissipative properties (different in nature) of the material, shows that the combined consideration of all these properties brings the resulting pattern closer to the one observed in reality. That is, the amplitude of the structure’s oscillations does not grow infinitely, but gradually decreases over time, and the maximum possible consideration of nonlinear and dissipative properties leads to the fastest damping of oscillations.

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Section: Introductionmentioning

confidence: 99%

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

et al. 2021

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Fractional visco‐elastic Timoshenko beam deflection via single equation

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Lorenzo

et al. 2015

Numerical Meth Engineering

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SUMMARYThis paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald-Letnikov approximation of the fractional derivative.Moreover, Timoshenko beam response is generally evaluated by solving a couple of differential equations. In this paper, expressing the equation of the elastic curve just through a single relation, a more general procedure, which allows the determination of the beam response for any load condition and type of constraints, is developed.

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