Stability and chaotic motion in columns of nonlinear viscoelastic material

陈立群,; 程昌钧,; Chen, Liqun; Chang-jun, Cheng

doi:10.1007/bf02459307

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…The nonlinear dynamical behavior of piles has been researched in [5]. In addition, Suire and Cederbaum [6] , Chen and Cheng [7] analyzed the stability and chaotic motion in columns composed of nonlinear viscoelastic materials. Hu and Cheng [8] researched the vertical chaotic motion of viscoelastic piles.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic characteristics of piles embedded in rock

Chun-lin

Chang-jun

Sheng-gang

2007

J. of Shanghai Univ.

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The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincaré sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic characteristics of piles embedded in rock

Chun-lin

Chang-jun

Sheng-gang

2007

J. of Shanghai Univ.

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“…Therefore, many studies [1][2][3][4][5][6][7][8][9][10][11][12][13] have been performed on the nonlinear dynamics of viscoelastic structures. Chen et al [2][3][4][5] investigated the dynamic stability and chaotic motion of a nonlinear viscoelastic beam and column by applying the Leaderman constitutive relation with Galerkin numerical integration. Also, other constitutive relations [6][7][8] are adopted to investigate the dynamics of the viscoelastic structures.…”

Section: Introductionmentioning

confidence: 99%

“…Also, other constitutive relations [6][7][8] are adopted to investigate the dynamics of the viscoelastic structures. Moreover, there has been considerable interest in the study of the nonlinear dynamics of the beam [2][3][6][7][8] , column [4][5] , pile [9][10] , plate [11] , shell [12] , and string [13] etc. However, few studies are focused on the nonlinear dynamic behavior of a viscoelastic shallow arch.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic behaviors of viscoelastic shallow arches

Wang

Zhao

2009

Appl. Math. Mech.-Engl. Ed.

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The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches subjected to external excitation are investigated. Based on the d'Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical integration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch are investigated. The results show that viscoelastic shallow arches may appear to have a chaotic motion for certain conditions.

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Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm

Sun

Chen

2021

Chaos, Solitons & Fractals

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Stability and chaotic motion in columns of nonlinear viscoelastic material

Cited by 5 publications

References 11 publications

Nonlinear dynamic characteristics of piles embedded in rock

Nonlinear dynamic characteristics of piles embedded in rock

Nonlinear dynamic behaviors of viscoelastic shallow arches

Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm

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