Free transverse vibration of nonlocal viscoelastic orthotropic multi-nanoplate system (MNPS) embedded in a viscoelastic medium

Karličić, Danilo; Kozić, Predrag; Pavlović, Ratko

doi:10.1016/j.compstruct.2014.04.002

Cited by 64 publications

(20 citation statements)

References 38 publications

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“…Nevertheless, from the physical point of view expressions (34a) and (34b) represents natural frequency and critical buckling load of a single simply supported orthotropic nanoplate. This is in line with the results of previous works by Karličić et al [49] and Ansari et al [57].…”

Section: Comparative Studysupporting

confidence: 94%

“…Considering that all nanoplates in the system are simply supported, assumed solution for transversal displacements of i-th nanoplateis of the following form where , ; and are amplitudes and natural frequencies, respectively. In the papers presented by Karličić et al [49] and Reddy [59] it is shown that assumed displacement field satisfies the given boundary conditions, and it is independent of the influence of other nanoplates in MNPS.…”

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 94%

“…In the recently published works by Karličić et al [49] and Stojanović et al [52], the methodology to obtain analytical solutions for natural frequencies and critical buckling loads of complex systems of homogeneous and elastic beams and plates is suggested. Based on these results, we supposed the solution of ith algebraic equation in the system (17) …”

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 99%

See 2 more Smart Citations

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Karličić

Cajić

Kozić

et al. 2015

Composite Structures

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Section: Comparative Studysupporting

confidence: 94%

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 94%

Section: Problem Formulation and Closed Form Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Karličić

Cajić

Kozić

et al. 2015

Composite Structures

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“…It is commonly known that the lowest natural frequency and buckling load of systems of a larger number of coupled nano/micro structures correspond to the natural frequency and buckling load of one beam or plate, see Karliţiš et al [31]. In this paper, the results for the lowest natural frequency and critical buckling load of the EBDMBS may be compared with those obtained for a microbeam one, presented in Ke et al [24] and Ma et al [19].…”

Section: Thermal Effect On the Natural Frequency Of The Ebdmbsmentioning

confidence: 86%

Thermal Effect on Free Vibration and Buckling of a Double-Microbeam System

Atanasov¹,

Karličić²,

Kozić³

et al. 2017

FU Mech Eng

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“…The system of coupled partial differential equations was solved by the generalized differential quadrature method and natural frequencies of multi-layered graphene sheets were obtained for different boundary conditions. Karličić et al [44] studied the free vibration of viscoelastic multi-nanoplate system coupled in a viscoelastic medium based on the nonlocal viscoelastic theory. They obtained analytical solutions for the natural frequency and modal damping of multi-nanoplate system for the arbitrary number of nanoplates in the system and also showed the influence of various material and geometrical parameters on the complex natural frequencies.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration and stability of a multiple-nanobeam system coupled by the Winkler elastic medium

Karličić

Kozić

Pavlović

2016

Applied Mathematical Modelling

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Highlights Multiple-nanobeam system is analyzed by Eringen nonlocal theory.  The nonlocal Euler -Bernoulli beam theory is proposed in this study.  The MNBS is simply supported and under the influence of axial load.  The natural frequencies and the critical buckling load are obtained. Abstract:The nonlocal Euler -Bernoulli beam theory is proposed for the free vibration and stability analyses of a multiple-nanobeam system (MNBS) using the Eringen nonlocal continuum theory. It is assumed that every nanobeam in the system of multiple-nanobeams is simply supported and under the influence of axial load. The MNBS is embedded in the Winkler elastic medium. The motion of the system is described by a set of m homogeneous partial differential equations, which are derived by using D'Alembert's principle. Analytical solutions of free vibrations and buckling for a multiple-nanobeam system are obtained by using the classical Bernoulli-Fourier method and trigonometric method, for the case of the identical nanobeam. To validate the accuracy of application of trigonometric methods for a determined natural frequency and buckling load of MNBS, numerical solution of the characteristic polynomial are also conducted for a different number of nanobeams. Moreover, the finite difference method is employed to solve the system of partial differential equations of motion of MNBS, where good agreement with the analytical results is achieved. Numerical studies show the effect of the nonlocal parameter, stiffness of Winkler elastic medium and number of nanobeams for the free transversal vibration and buckling of MNBS. The presented analyses are very useful for the study and design of the nanoelectromechanical systems such as nano-resonators.

show abstract

Free transverse vibration of nonlocal viscoelastic orthotropic multi-nanoplate system (MNPS) embedded in a viscoelastic medium

Cited by 64 publications

References 38 publications

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

Thermal Effect on Free Vibration and Buckling of a Double-Microbeam System

Nonlocal vibration and stability of a multiple-nanobeam system coupled by the Winkler elastic medium

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