Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories

Ghorbani, Khashayar; Mohammadi, Kianoosh; Rajabpour, Ali; Ghadiri, Majid

doi:10.1016/j.jpcs.2018.12.038

Cited by 39 publications

(12 citation statements)

References 70 publications

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“…It was founded that a remarkable difference was obtained in cases of with and without surface effects for both local and nonlocal theories. It is found that material length scale (MLS) parameter and NL increases and decreases the natural frequency, respectively, and the effects of surface properties on responses are stronger in higher values of MLS parameter and lower values of the NL (Ghorbani et al, 2019). In analysis of nonlinear dynamics of a double-layer piezoelectric and Kelvin–Voigt viscoelastic nanobeams, it is concluded that with surface energy effect, the softening behavior of the lower nanobeam is slightly weakened, whereas the softening-type behavior of the upper nanobeam becomes more intense in the presence of the surface effect (Rahmanian and Hosseini-Hashemi, 2019).…”

Section: Introductionmentioning

confidence: 99%

The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator

Kachapi

Daniali

Dardel

et al. 2020

Journal of Intelligent Material Systems and Structures

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In current work, Gurtin–Murdoch surface/interface and nonlocal theories are presented to investigate nonlinear vibration and stability analysis of piezoelectric nanoresonator simultaneously subjected to direct and alternating voltages. Complex averaging method combined with arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the piezoelectric nanoresonator. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibration response of the piezoelectric nanoresonator. Also, with increasing dimensionless nonlocal parameter and decreasing nanoshell stiffness, dimensionless natural frequency, the resonance amplitude, the range of instability with saddle-node bifurcations and nonlinear hardening behavior, and also resonance frequency decrease. In addition, it is found that when the surface/interface effects corresponding to higher surface/interface density are considered, natural frequency is increased. Also, regardless the Lamé’s constants lead to decreasing of piezoelectric nanoresonator stiffness, and as a result, the dimensionless natural frequency is lower than all cases. The rest of the surface/interface parameters do not have much effect on the dimensionless natural frequency. Also, with increasing electrostatic and piezoelectric voltages, the oscillation amplitude and range of the piezoelectric nanoresonator system’s instability and all nonlinear behavior of piezoelectric nanoresonator are increased.

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Section: Introductionmentioning

confidence: 99%

The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator

Kachapi

Daniali

Dardel

et al. 2020

Journal of Intelligent Material Systems and Structures

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“…As the third example, a comparative study is performed to verify the accuracy of the present model in capturing size effects. For this objective, Table 3 tabulates the dimensionless natural frequencies of a homogenous nanoscale cylindrical shell with SS-SS and C-C boundary conditions predicted by the present work and Ghorbani et al [58] . Results are presented for different values of nonlocal parameter and material length scale parameter with and without surface effects.…”

Section: Comparative Studymentioning

confidence: 99%

“…Therefore, there is a scientific need to explore the combined effects of nonlocal stress, strain gradient, and surface energy by using NSGT in conjunction with the surface elasticity theory. Recently, the combined effect of nonlocal stress, strain gradient, and surface energy on the mechanical behaviors of homogenous nanoplates and nanoshells have been addressed by some researchers [56][57][58] . However, to the best of the authors' knowledge, no works have been concerned with combining NSGT with surface elasticity theory to assess the size effects in FG nanoshells so far.…”

Section: Introductionmentioning

confidence: 99%

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

Zhu

Guo

et al. 2019

Appl. Math. Mech.-Engl. Ed.

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In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

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“…Fang et al [75] combined the Goldenveizer-Novozhilov shell theory with surface elastic continuum mechanics for size-dependent free vibration analysis of piezoelectric double-shell nanostructures. Ghorbani et al [76] explored the surface stress effect as well as nonlocality and strain gradient sizedependency on the free vibration response of cylindrical nanoshells. Wang et al [77] investigated the nonlinear dynamics of fluid-conveying FG sandwich nanoshells based upon the surface stress elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

Xie

Sahmani

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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As one of the innovative materials, functionally graded (FG) composite materials have the capability to vary microstructure and design attributes from one side to other representing the desired material properties. The prime aim of this work is to analyze the surface stress effect on the nonlinear free vibration response of FG cylindrical nanoshells incorporating various modal interactions. To this end, the Gurtin-Murdoch theory of elasticity together with the von Karman geometrical nonlinearity is implemented to the classical shell theory to construct an efficient size-dependent shell model. In order to take the modal interactions between the main oscillation mode and various symmetric vibration modes, the lateral deflection of the FG nanoshell is expressed as combination of the simple main vibration mode and convergent symmetric modes. Thereafter, the solution of problem is considered as the summation of the homogenous and particular parts to put the Galerkin technique to use. Finally, the multiple timescales method is employed to achieve analytical expression for the surface elastic-based frequency response of FG nanoshells. It is displayed that in the presence of modal interaction, by increasing the shell deflection, the value of the frequency ratio decreases while in the absence of modal interaction, it enhances.

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Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories

Cited by 39 publications

References 70 publications

The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator

The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

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