Some dynamical properties of a viscoelastic cylindrical shell

丁睿,; 朱正佑,; 程昌钧,; Ding, Rui; Zhu, Zhihui; Chang-jun, Cheng

doi:10.1007/bf02463847

Cited by 3 publications

(7 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the relaxation core of the integral operator is denoted as R(t − τ), the constitutive equations of FG-VE-Ps in the framework of the Boltzmann-Volterra principle are modeled as follows [1,5,41]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…Assuming that the edges of an FG-VE plate on a VE-F are simply supported, the solution of the basic equations is sought as follows [1,5,41]:…”

Section: Solution Proceduresmentioning

confidence: 99%

“…In Figures 3 and 4, the time-dependent change of w 1 (t 1 ) is calculated numerically using the Maple program for Equation (19) to verify the accuracy of Equations ( 23) and (26), where the critical time values are obtained. In numerical calculations, the following data are used: a = 50h, a = 2b, γ = 0.5, p VF = 0.7, K 0 = 4.2 × 10 7 (N/m 3 ), [3][4][5]27,33,41]. The units for the VE-Fs are also valid for the subsequent tables and figures.…”

Section: Numerical Analysismentioning

confidence: 99%

“…General questions of the theory of viscoelasticity are considered in the fundamental works [1][2][3], including the constructions of hereditary relations between stresses and strains, the reciprocity of such relations, methods of analyzing the kernels of creep and relaxation, and methods for solving static and dynamical problems. The applied problems of the theory of viscoelasticity, including the construction of continuous and discrete models of homogeneous viscoelastic plates, are considered in [4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

Sofiyev

2023

Mathematics

View full text Add to dashboard Cite

The widespread use of structural elements consisting of functionally graded (FG) materials in advanced technologies has led to extensive research. Due to the difficulties encountered during modeling and problem solving, the number of studies on the dynamic behavior of structural elements made of FG viscoelastic materials is quite limited compared to the number examining FG elastic materials. This study is one of the first attempts to solve the dynamical problem by the mathematical modeling of functionally graded viscoelastic plates (FG-VE-Ps) and viscoelastic media together with different initial conditions. FG-VE-Ps on viscoelastic foundations (VE-Fs) are assumed to be under compressive edge load in the longitudinal direction. The governing equations for FG-VE-Ps on VE-Fs are derived using Boltzmann and Volterra concepts. The problem is reduced to the solution of integro-differential equation system using the Galerkin method. Then, by performing Laplace transforms, new analytical expressions for the time-dependent deflection function and critical time at different initial conditions are found. The loss of stability of FG-VE-Ps on VE-Fs is modeled to cover three time-varying ranges: the first is the range in which the deflection function decreases; the second is the transition interval; the third is the increase range of deflection function, which leads to the loss of stability. The time corresponding to the sharp increase of the deflection function is defined as the critical time, and is determined both theoretically and numerically. The results are compared with the results obtained by various methods to confirm their accuracy. Finally, the effects of VE-Fs, VE material properties, and FG profiles on the critical time behavior of plates are studied numerically.

show abstract

Section: Governing Equationsmentioning

confidence: 99%

“…Assuming that the edges of an FG-VE plate on a VE-F are simply supported, the solution of the basic equations is sought as follows [1,5,41]:…”

Section: Solution Proceduresmentioning

confidence: 99%

Section: Numerical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

Sofiyev

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Chen Liqun at al [6] assumed the viscoelastic material of beam obey the fractional derivative constitutive relation and investigated the forced vibrations of viscoelastic beam under periodic excitations. Zhu Zhengyou at al [7] derived the equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam and the material of beam is assumed to obey a three-dimensional fractional derivative viscoelastic constitutive relation. In this paper, we will study the quasi-static mechanical behavior of Euler-Bernoulli beam based on the theory of fractional derivative viscoelastic model.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Static Analysis of Beam Described by Fractional Derivative Kelvin Viscoelastic Model under Lateral Load

Yao

Liu

Yan

2011

AMR

View full text Add to dashboard Cite

The beam is assumed to obey a three-dimensional viscoelastic fractional derivative constitutive relations, the mathematical model and governing equations of the quasi-static and dynamical behavior of a viscoelastic Euler-Bernoulli beam are established, the quasi-static mechanical behavior of Euler-Bernoulli beam described by fractional derivative model is investigated, and the analytical solution is obtained by considering the properties of the Laplace transform of Mittag-Leffler function and the properties of fractional derivative. The result indicate that the quasi-static mechanical behavior of Euler-Bernoulli beam described by fractional derivative viscoelastic model can reduced to the cases of classic viscoelastic and elastic, the order of fractional derivative has great effect on the quasi-static mechanical behavior of Euler-Bernoulli beam.

show abstract

On the solution of the dynamic stability of heterogeneous orthotropic visco-elastic cylindrical shells

Sofiyev

2018

Composite Structures

View full text Add to dashboard Cite

Some dynamical properties of a viscoelastic cylindrical shell

Cited by 3 publications

References 3 publications

On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

Quasi-Static Analysis of Beam Described by Fractional Derivative Kelvin Viscoelastic Model under Lateral Load

On the solution of the dynamic stability of heterogeneous orthotropic visco-elastic cylindrical shells

Contact Info

Product

Resources

About