Forced vibration of nanoplate on viscoelastic substrate with consideration of structural damping: An analytical solution

Hosseini-Hashemi, Shahrokh; Mehrabani, H.; Ahmadi-Savadkoohi, A.

doi:10.1016/j.compstruct.2015.07.068

Cited by 22 publications

(3 citation statements)

References 30 publications

(35 reference statements)

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“…Hashemi et al [22] investigated the forced vibration of a rectangular isotropic viscoelastic single layer grapheme sheets resting on a viscoelastic foundation by using an analytical method. The Navier solution method was used in this study to get the response and the dynamic deflection of the simply supported nanoplates with a distributed load.…”

Section: Forced Vibrationmentioning

confidence: 99%

Analysis and vibration of rectangular nanoplates - An overview

Eraky

Salama

Abdelhameed

2021

The Egyptian International Journal of Engineering Sciences and

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This work presents a review on solution methods and analysis of nanoplates structures with different boundary conditions and load cases, under some effects such as magnetic field and the effect of other parameters on the vibration and analysis. Moreover, it represents a review about the theories that are used to study these nanoplates structures such; the nonlocal elasticity theory by Eringen which is introduced to take into consideration the small scale effect of such nano-structure. The equation of motion of the nanoplate is derived then it used to study this type of nano-structures. Nanoplates are used in a lot of branches of life and in different applications because of the high and excellent mechanical, thermal and electrical properties of these nanoplates. Applications of nanoplate structure are also introduced to show the importance of studying and getting a solution of such nanoplates. Also, some parametric studies are discussed to show the effect of the studied parameters on the dynamic behaviour and analysis of these nanoplates.

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Section: Forced Vibrationmentioning

confidence: 99%

Analysis and vibration of rectangular nanoplates - An overview

Eraky

Salama

Abdelhameed

2021

The Egyptian International Journal of Engineering Sciences and

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“…In the study performed by Hosseini Hashemi et al 39 the nonlocal elasticity theory was utilized to find the forced vibrational behavior of a nano-plate made of viscoelastic material resting on a viscoelastic base. Karlıˇcı´c et al 40 assessed the longitudinal vibration of a double-nano-rod system made of viscoelastic material.…”

Section: Introductionmentioning

confidence: 99%

Free vibration characteristics of viscoelastic nano-disks based on modified couple stress theory

Alizadeh

Shishesaz

Shahrooi

et al. 2022

The Journal of Strain Analysis for Engineering Design

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This paper investigates the vibrational behavior of a viscoelastic and size-dependent nano-disk based on the modified couple stress theory (MCST). The material characteristics in nano-scale are modeled according to Zener viscoelastic constitutive relation. In addition, displacement components are defined based on classical plate theory. Leaderman integral is also used to determine the viscous parts of the stress tensor. Hamilton’s principle is utilized to derive the governing equations of motion for specifying the strain, kinetic energy, and viscous work. The obtained equations are discretized with the help of the Galerkin method and decoupled through the diagonalization procedure. Laplace transformation is employed to solve the resulting equations in differential–integral form. The damping ratio, the imaginary part and real part of the Eigen frequency of the considered nano-disk are calculated to investigate the effects of influential parameters on the nano-disk vibrational behavior. These parameters include nonlocal parameter boundary conditions, geometric constant, power constant, and element relaxation coefficient. Results obtained on different mode shapes indicate that increasing the dimensionless element relaxation coefficient is followed by a decrease in the imaginary part of the Eigen frequency regarding the energy dissipation as well as a decrease in the real part of the Eigen frequency. Furthermore, increasing the h/l ratio is accompanied by variations in the imaginary part, real part, and damping ratio. According to the results, the effect of damping on vibrational behavior of the nano disk is more distinguished for smaller values of h/l.

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“…Basedon the sinusoidal shear deformation theory and by using the Navier's and meshless methods, free vibrationanalyses of viscoelastic double-bonded polymeric nanocomposite plates are investigated byMohammadimehr et al (2015). Forced vibration analysis of a single layer viscoelastic graphene sheetresting on viscoelastic medium was performed by Hosseini Hashemi et al (2015). The governing equationis derived using Hamilton's principle based on the classical plate theory and viscoelastic KelvinVoigt model.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

Molla-Alipur

Rajabi

2017

Lat. Am. j. solids struct.

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Effects of viscoelastic substrates on the sandwich structures oscillations are examined in this paper. In this regard, dynamic response of sandwich annular panels with FG polar orthotropic face sheets resting on viscoelastic substrate is presented. Young's modulus in the radial and circumferential direction, shear modulus and density of each face sheet may be varied continuously in the radial direction. The viscoelastic substrate is modeled as Kelvin-Voigt foundation. To describe more accurately response of sandwich structures, the governing dynamical equations are derived based on the layerwise theory and five systems of second order coupled partial differential equations are obtained. The effects of the stiffness and damping coefficients of the foundation on the dynamic behavior of sandwich plate are investigated for various transient loads and boundary condition. Since no available results may be found in literature to demonstrate the efficiency and accuracy of the obtained results, the obtained results are verified by comparison with finite element results based on the three dimensional theory of elasticity for some special cases.

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Forced vibration of nanoplate on viscoelastic substrate with consideration of structural damping: An analytical solution

Cited by 22 publications

References 30 publications

Analysis and vibration of rectangular nanoplates - An overview

Analysis and vibration of rectangular nanoplates - An overview

Free vibration characteristics of viscoelastic nano-disks based on modified couple stress theory

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

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