Dynamic stability of nonlocal Voigt–Kelvin viscoelastic Rayleigh beams

Pavlović, Ivan; Pavlović, Ratko; Ćirić, Ivan; Karličić, Danilo

doi:10.1016/j.apm.2015.02.044

Cited by 24 publications

(12 citation statements)

References 20 publications

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“…Some other researchers through combining viscoelasticity theory with theories related to micro and nano structures studied the vibration behavior of viscoelastic nanobeams [22][23][24][25]. In this regard, based on the nonlocal Timoshenko beam model and thermal elasticity, Ghavanloo and Fazelzadeh [26] , are defined as [7] (1)…”

Section: Introductionmentioning

confidence: 99%

Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory

Ansari

Oskouie

Sadeghi

et al. 2015

Physica E: Low-dimensional Systems and Nanostructures

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Section: Introductionmentioning

confidence: 99%

Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory

Ansari

Oskouie

Sadeghi

et al. 2015

Physica E: Low-dimensional Systems and Nanostructures

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“…In this section, analytical results are firstly compared with the numerical results obtained from the Monte Carlo simulation with the aim of justifying the use of the direct Liapunov method for this system. The Monte Carlo simulation method is widely used [19,20] and it is very important in assessing the validity of the approximate analytical results. Now, according to the numerical procedure presented in [21], relation (3.5) is substituted in Eqs.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation

Pavlović

2018

Theor appl mech (Belgr)

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The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure.2010 Mathematics Subject Classification: 74H55.

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“…Buckling of viscoelastic nanobeams can be seen in Figs. (6) and (7). NDF drops to zero with increasing effect of axial load.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…In Eqs. (6) and 7, boundary conditions should be written in matrix form using amplitude function in Eq. (8) for unknown coefficients as below: Eq.…”

Section: Nonlocal Equation Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…Lei et al investigated the dynamic behavior of nonlocal viscoelastic Euler-Bernoulli [3] and Timoshenko nanobeams [4]. Dynamic stability and buckling of viscoelastic nanobeams studied by Chen et al [5] and Pavlovic et al [6]. Buckling of cantilever nanotubes [7,8], boron-nitride nanotubes [9] and silicon-carbide nanotubes [10] investigated by researchers.…”

Section: Introductionmentioning

confidence: 99%

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Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam

Arda

2018

International Journal of Engineering and Applied Sciences

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Vibration of an axially loaded viscoelastic nanobeam has been studied in this paper. Viscoelasticity of the nanobeam has been modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for an axially compressed nanobeam has been obtained with help of Eringen's Nonlocal Elasticity Theory. Viscoelasticity effect on natural frequency and damping of nanobeam and critical buckling load have been investigated. Nonlocality effect on nanobeam structure in the view of viscoelasticity has been discussed.

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Dynamic stability of nonlocal Voigt–Kelvin viscoelastic Rayleigh beams

Cited by 24 publications

References 20 publications

Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory

Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory

Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation

Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam

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