Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads

An, Fengxian; Chen, Fangqi

doi:10.1016/j.chaos.2016.05.006

Cited by 16 publications

(1 citation statement)

References 22 publications

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“…Dynamic stability of the viscoelastic plates with longitudinally varying tensions subjected to axial acceleration was studied by Tang et al (2016). In addition, An and Chen (2016) studied the nonlinear dynamic behavior of the viscoelastic plates subjected to external force and subsonic flow. They found the critical conditions that chaos could take place.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory

Ajri

Fakhrabadi

Rastgoo

2018

Lat. Am. j. solids struct.

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This paper analyses the non-stationary free vibration and nonlinear dynamic behavior of the viscoelastic nano-plates. For this purpose, a sizedependent theory is developed in the framework of the consistent couple stress theory for viscoelastic materials. The previously presented modified couple stress theory was based on some consideration making it partially doubtful to apply. This paper uses the recent findings for the mentioned problem and develops it to analyze the nonlinear dynamic behavior of nanoplates with nonlinear viscoelasticity. The material is supposed to follow the Leaderman integral nonlinear constitutive relation. In order to capture the geometrical nonlinearity, the von-Karman strain displacement relation is used. The viscous parts of the size-independent and size-dependent stress tensors are calculated in the framework of the Leaderman integral and the resultant virtual work terms are obtained. The governing equations of motion are derived using the Hamilton principle in the form of the nonlinear second order integro-partial differential equation with coupled terms. These coupled size-dependent viscoelastic equations are solved using the forthorder Runge-kutta and Harmonic balance method after simplifying by the expansion theory. The short-time Fourier transform is performed to examine the system free vibration. In addition, frequency-and forceresponses of the nanosystem subjected to distribute harmonic load are presented. The obtained results show that the viscoelastic model-based vibration is non-stationary unlike the elastic model. Moreover, the damping mechanism of the viscoelasticity is amplitude dependent and the contribution of the viscoelastic damping terms at higher forcing conditions becomes noticeable.

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Section: Introductionmentioning

confidence: 99%