Dynamical behavior of nonlinear viscoelastic beams

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

doi:10.1007/bf02459308

Cited by 15 publications

(9 citation statements)

References 7 publications

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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%

“…where I = A z 2 dA, J 4 = A z 4 dA, the prime denotes the derivation with x, the overdot denotes the derivation with t,Ḋ(t) =Ė(t)/E 0 , and D(t) can be assumed as [2][3] …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamic behaviors of viscoelastic shallow arches

Wang

Zhao

2009

Appl. Math. Mech.-Engl. Ed.

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“…The Galerkin method is generally adopted to study the quasi-static and dynamical behaviors of viscoelastic Euler-Bernoulli beams and Timoshenko beams, in which the constitutive relations of the material usually are differential type [1] , Boltzmann superposition type [2] or Leaderman type [3] . Akoz and Kadioglu [2] applied the correspondence principle and a numerical inverse transform method to discuss the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam.…”

Section: Introductionmentioning

confidence: 99%

Quasi-static analysis for viscoelastic Timoshenko beams with damage

2006

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Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.

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“…In Ref. [5], Chen and Cheng studied the dynamical behavior of nonlinear viscoelastic Euler-Bernoulli beams, where, the material of the beam was assumed to obey the Leaderman nonlinear constitutive relation. Li and Zhu [6"7] investigated the dynamical behavior of nonlinear viscoelastic Timoshenko beams with a fractional derivative model.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of nonlinear viscoelastic Timoshenko beams with damage on a viscoelastic foundation

Dong-fa

Zhang

Chang-jun

2004

J. of Shanghai Univ.

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Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partiai differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.

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Dynamical behavior of nonlinear viscoelastic beams

Cited by 15 publications

References 7 publications

Nonlinear dynamic behaviors of viscoelastic shallow arches

Nonlinear dynamic behaviors of viscoelastic shallow arches

Quasi-static analysis for viscoelastic Timoshenko beams with damage

Dynamical behavior of nonlinear viscoelastic Timoshenko beams with damage on a viscoelastic foundation

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