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

Mohammadimehr, Mehdi; Monajemi, A. A.; Moradi, Mehdi

doi:10.1007/s12206-015-0522-2

Cited by 38 publications

(13 citation statements)

References 37 publications

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“…6. The difference and change of the thermal and mechanical parameters that identify the elastic foundation have a major effect on the profiles of deflection and temperature (see Mohammadimehr, (2015). 7.…”

Section: Effect Of Winkler's Elastic Foundation On the Studied Fieldsmentioning

confidence: 99%

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Abouelregal

2020

Journal of Vibration and Control

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In the current investigation, the thermoelastic vibration of a viscoelastic microbeam resting on the Winkler foundation is studied using the fractional-order theory. To describe the damping of the viscoelastic material according to experimental results, the Kelvin–Voigt model is replaced by a new form with a fractional-order derivative. The generalized thermoelasticity model and Euler–Bernoulli beam theory are used to construct the governing equation. The microbeam is subjected to axial load, ultrafast laser heating, and varying sinusoidal heat. The governing equation is then solved using the Laplace transform technique to determine the deflection and thermoelastic interaction responses of microbeams. The effects of many parameters such as the coefficient of viscosity, axial load, fractional derivative order, laser pulse duration, and foundation parameter on the microbeam response are explained and discussed in detail.

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Section: Effect Of Winkler's Elastic Foundation On the Studied Fieldsmentioning

confidence: 99%

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Abouelregal

2020

Journal of Vibration and Control

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“…The Maxwell model, the Kelvin-Voigt model and the standard linear solid model are applied to forecast material's response subjected to different loading conditions. According to the MSGT, Mohammadimehr et al [38] carried out the free vibration of tapered viscoelastic microrod embedded on the Kelvin-Voigt visco-Pasternak foundation. Zenkour [39] accomplished the transient thermal analysis of single layer graphene sheet on viscoelastic substrate.…”

Section: Ghorbanpour Arani and Shokravimentioning

confidence: 99%

Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

Jamalpoor

Bahreman

Hosseini

2017

Jnl of Sandwich Structures & Materials

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In this paper, an analytical process is proposed to investigate the size-dependent free vibration of orthotropic multi-viscoelastic microplate systems (OMVMPS) embedded in Kelvin–Voigt visco-Pasternak medium according to the modified strain gradient theory. Governing equations of motion in the partial form and the related boundary conditions are derived by utilizing the Kirchhoff plate theory and Hamilton’s variational principle. The two different sorts of “chain” boundary conditions like “clamped Chain” and “free chain” systems are considered for the ends of microplate system. Navier’s method, which convinces that the simply supported boundary conditions and trigonometric methods are applied to analytically investigate the size effect of the natural frequencies of OMVMPS. The numerical outcomes are offered to report the variation of OMVMPS natural frequencies with the numerous amounts of the microplate numbers, the length scale parameter, aspect ratio, visco-Pasternak foundation parameters, the thickness of microplate, and higher modes number. Several numerical outcomes of this research depict that when the number of microplates is low, there is a significant distinction between natural frequencies achieved for “clamped chain” and “free chain” systems. Also, it is demonstrated that by increasing the number of microplates, the effect of the visco-Pasternak substrate on the natural frequency of system vibration decreases.

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“…46 Mohammadimehr et al. 47 studied the vibration analysis of viscoelastic tapered micro-rod based on the strain gradient theory resting on visco-Pasternak foundation using DQM.…”

Section: Introductionmentioning

confidence: 99%

“…Buckling analysis of the power-law sandwich plates with FG skins using a new quasi-3D hyperbolic sine shear deformation theory is discussed by Neves et al 43 Ghorbanpour Arani et al 44 described the Pasternak effect on the buckling of embedded SWCNTs using nonlocal cylindrical shell theory. The strength, stability, and deflection of sandwich structures with an aluminum foam core are investigated by Magnucki and Szyc 45 and Magnucki et al 46 Mohammadimehr et al 47 studied the vibration analysis of viscoelastic tapered microrod based on the strain gradient theory resting on visco-Pasternak foundation using DQM.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method

Mohammadimehr

Shahedi

Navi

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, the magneto-mechanical nonlinear vibration behavior of rectangular functionally graded carbon nanotube reinforced composite (FG-CNTRC) sandwich Timoshenko beam based on modified couple stress theory (MCST) is investigated by the generalized differential quadrature method. The FG-CNTRC sandwich beam consists of two FG-CNTRC face sheets and homogenous core subjected to longitudinal magnetic field. In the FG-CNTRC face sheets, carbon nanotubes are disseminated in different patterns as uniform distribution, FG-X, FG-V, and FG-O. Based on von Kármán geometric nonlinearity, the nonlinear governing equations are derived by the Hamilton’s principle. Accuracy and convergence of this study are validated by comparing the numerical results with those found in literature. Various parameters effects are examined on the nonlinear 1st frequency of the sandwich beam. The results reveal that composition of the CNTRC face sheets and homogenous core in sandwich beam can be achieved remarkable stiffness in comparison to only CNTRC beam or only homogenous beam. For achieving the highest stiffness of FG-CNTRC sandwich beam, the value of thickness ratio is obtained about 0.34 and 0.27 in the presence and absence of Pasternak foundation, respectively. Moreover, the linear and nonlinear 1st frequencies increase with an increase in the magnetic field for all of CNT distribution types of sandwich beam and different boundary conditions whereas the frequency ratio decreases. Also the highest and lowest nonlinear 1st frequencies are corresponding to FG-A and FG-V distributions of CNT in face sheets, respectively.

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

Cited by 38 publications

References 37 publications

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method

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