Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium

Pouresmaeeli, S.; Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad

doi:10.1016/j.compstruct.2012.08.051

Cited by 140 publications

(56 citation statements)

References 19 publications

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“…The scale coefficient μ is taken between 0nm and 2nm herein. The dimensionless damping ratio G/G 0 is taken as that in [46], and it can be expressed as G = g a 2 D ρh . In this subsection, without special declaration, the biaxial compression ratio is taken as δ = 1.…”

Section: Effect Of Nonlocal Parameter On Biaxially Compressed Dlnpmentioning

confidence: 99%

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Nonlocal effect on the nonlinear dynamic characteristics of buckled parametric double-layered nanoplates

Wang

2016

Nonlinear Dyn

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The homoclinic phenomena in doublelayered nanoplates (DLNP) are investigated. Based on the nonlocal continuum theory, the nonlinear dynamical equations for DLNP subjected to in-plane excitation are derived by double-mode Galerkin truncation. The extended Melnikov method is utilized to discuss the homoclinic phenomena and chaotic motion for the buckled DLNP system. The criterions for the existence of transverse homoclinic orbits are established under different four buckling cases (i.e., the first-and second-type synchronous buckling as well as asynchronous buckling). And the results derived by the abovementioned analysis are verified by molecular dynamics and Lyapunov exponent spectrum. Small-scale effect on the homoclinic motion is mainly inspected. From the result, it is rather novel that the transversality condition is independent of the nonlinear terms in the equations. This fact means that it is not necessary to distinguish whether the boundaries are movable or immovable for the in-plane parametric excitation DLNP. The parametric regime where homoclinic phenomena appear shrinks with the augment of nonlocal parameter for the first-type synchronous buckling case. However, this trend is just opposite for the other three buckling cases.Finally, it can be seen that homoclinic phenomena more likely occur on Mode I (i.e., lower mode) for the second-type synchronous and asynchronous buckling cases. However, the homoclinic motion for the firsttype asynchronous buckling most likely takes place on Mode III.

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Section: Effect Of Nonlocal Parameter On Biaxially Compressed Dlnpmentioning

confidence: 99%

“…As for the viscoelastic nanoplates [46], the constitutive equation, i.e., Eq. (2), can be written as the following form:…”

Section: Equations Of Motion For Dlnp By Nonlocal Theorymentioning

confidence: 99%

Nonlocal effect on the nonlinear dynamic characteristics of buckled parametric double-layered nanoplates

Wang

2016

Nonlinear Dyn

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“…The authors applied the Galerkin approach to convert the partial differential governing equation into a set of eigenvalue equations. Also, using the Navier method, a closed-form expression for complex frequency of viscoelastic orthotropic plates resting on Kelvin-Voigt viscoelastic foundation based on the nonlocal elasticity theory of Eringen was demonstrated by Pouresmaeeli et al [25].…”

Section: Introductionmentioning

confidence: 98%

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

2016

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In this study, nonlocal elasticity theory in conjunction with Gurtin-Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a viscoPasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton's principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

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“…They showed that the real part of the natural frequencies decreases generally with an increase in the values of the nonlocal parameter. Pouresmaeeli et al [2] studied the vibration characteristics of a viscoelastic nanoplate using the nonlocal plate theory by including the effect of viscoelastic foundation. They solved this equation using Navier's type solution for simply supported nanoplate.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM

2015

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In the present work, based on strain gradient theory, the free vibration analysis of tapered viscoelastic micro-rod resting on viscoPasternak foundation is investigated. The material properties of micro-rod are assumed the visco-elastic and modeled as the Kelvin-Voigt. Using Hamilton's principle and energy method, the governing equation of motion of viscoelastic micro-rods is derived, then this obtained equation using the differential quadrature method (DQM) for different boundary conditions is solved. In this study, the effects of various parameters such as the structural damping coefficient, Winkler and Pasternak foundation modulli, damping coefficient of the elastic medium and material length scale parameters on the non-dimensional natural frequencies of viscoelastic micro-rod are investigated. The results show that with an increase in the Winkler and Pasternak coefficients, the natural frequency increases as well as the obtained nondimensional natural frequencies by MCST and SGT decrease by increasing the material length to radius ratio. It can be seen that the nondimensional frequency for SGT is higher than that of the other theories. It is shown that the non-dimensional frequencies increase by increasing the damping coefficient for all theories. Moreover, at the specified value of damping coefficient of the elastic medium, the variation of non-dimensional natural frequency is approximately smooth.

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Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium

Cited by 140 publications

References 19 publications

Nonlocal effect on the nonlinear dynamic characteristics of buckled parametric double-layered nanoplates

Nonlocal effect on the nonlinear dynamic characteristics of buckled parametric double-layered nanoplates

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM

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