Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro beam with moving mass

Arefi, Mohammad; Pourjamshidian, Mahmoud; Arani, A. Ghorbanpour

doi:10.1177/1099636216658895

Cited by 24 publications

(8 citation statements)

References 39 publications

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“…By substituting variations of the strain and electric field components and integration over the thickness of sandwich nanoplate, the variation of strain energy can be expressed as (24) in which N ij ; M ij are resultants of force and moments that are defined as…”

Section: Governing Equations Of Motionmentioning

confidence: 99%

“…A parametric study was presented to investigate effect of the small scale parameter, thicknesses layers, external electric and magnetic loads and mode numbers on critical buckling load of magneto-electro-elastic sandwich nanoplate. Nonlinear free and forced vibration analysis of sandwich micro beam carrying a moving mass resting on nonlinear Pasternak foundation was studied by Arefi et al 24 Euler-Bernouli model with considering nonlinear terms according to the Von-Karman strain-displacement relations and strain gradient elasticity theory was used to obtain governing equations of motion. Nonlinear ordinary differential equations were discretized by Galerkin's technique.…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear free and forced vibration analysis of sandwich micro beam carrying a moving mass resting on nonlinear Pasternak foundation was studied by Arefi et al. 24 Euler–Bernouli model with considering nonlinear terms according to the Von-Karman strain–displacement relations and strain gradient elasticity theory was used to obtain governing equations of motion. Nonlinear ordinary differential equations were discretized by Galerkin’s technique.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

Arefi

Arani

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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Comprehensive nonlocal piezoelasticity relations are developed in this paper for a sandwich functionally graded nanoplate subjected to applied electric potential based on higher-order shear and normal deformation theory. To account thickness stretching effect, the higher-order shear and normal deformation theory is developed. Based on this theory, the transverse deflection is decomposed into bending, shear and stretching portions in which the third term is reflected variation of transverse deflection along the thickness direction. Size dependency is accounted in governing equations based on nonlocal elasticity theory. The sandwich nanoplate is made of a functionally graded core integrated with two piezoelectric layers. Distribution of material properties are assumed according to the power-law function in the thickness direction. The Hamilton’s principle is used to derive governing equations of motion. Navier’s technique is implemented to solve partial differential equation of motion. Accuracy and efficiency of the presented technique are verified by a comparison between obtained results and existing results in literature for two cases including and excluding thickness stretching effect. The comparison between the results with and without thickness stretching effect can justify necessity of present work. Large parametric analysis is organized to investigate effect of significant parameters such as external applied voltage, nonlocal parameter, non-homogeneous index, stretching effect, length-to-thickness, length-to-width and core-to-face sheet thickness ratios on the vibrational behavior of the system. As an important result of this study, one can conclude that accounting thickness stretching effect leads to decrease of natural frequencies in comparison with cases disregards thickness stretching.

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Section: Governing Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

Arefi

Arani

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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show abstract

“…Based on Hamilton’s principle, the vibrational form of equations of motion can be written as [36]: in which, U , K , and Σ represent total strain energy, total kinetic energy, and external work of system, respectively.…”

Section: Equations Of Motion Based On Hamilton’s Principlementioning

confidence: 99%

Vibration behavior of visco-elastically coupled sandwich beams with magnetorheological core and three-phase carbon nanotubes/fiber/polymer composite facesheets subjected to external magnetic field

Arani

Zarei

Eskandari

et al. 2017

Jnl of Sandwich Structures & Materials

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In the present research, modeling and vibration analysis of the double of sandwich beams which are coupled by visco-Pasternak medium are investigated. Also, this system is rested on Winkler foundation. Sandwich beams consist of magnetorheological core and carbon nanotubes/fiber/polymer composite facesheets. The material properties of magnetorheological core are obtained using the experimental data available in literature. Halpin–Tsai model is utilized to determine the material properties of carbon nanotubes/fiber/polymer composite facesheets. Hamilton principle is used to obtain the equations of motion of this system. Based on Navier’s method, a closed-form solution is presented for free vibration analysis of coupled magnetorheological sandwich beams under simply supported boundary conditions. The effects of various parameters such as core-to-facesheets thickness ratio, length-to-thickness ratio, magnetic field intensity, volume fractions of carbon nanotubes, and fibers and visco-Pasternak coefficients on the natural frequencies and loss factors of coupled system are discussed. The results show that the modal loss factor, unlike natural frequency, decreases by increasing magnetic field intensity. These findings can be used in design and manufacturing of sandwich structures.

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“…Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments was studied by Shen and Xiang [22] that derived the motion equations based on higher-order shear deformation beam theory and concluded that thermal postbuckling path of unsymmetric FG-CNTRC beams is no longer the bifurcation type. Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro-beam with moving mass was performed by Arefi et al [23]. They illustrated the effect of some important parameters such as power gradient index, aspect ratio, position, and velocity of moving mass on the nonlinear natural frequency.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear high-order dynamic stability of AL-foam flexible cored sandwich beam with variable mechanical properties and carbon nanotubes-reinforced composite face sheets in thermal environment

Shahedi

Mohammadimehr

2017

Jnl of Sandwich Structures & Materials

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In this paper, the nonlinear dynamic stability analysis of sandwich beam including AL-foam flexible core and carbon nanotubes-reinforced composite face sheets subjected to axial periodic load are investigated by using generalized differential quadrature method. The flexible core of sandwich beam is made of Aluminum alloy foam with variable mechanical properties in the thickness direction. With considering the high-order geometrical nonlinearity in the core and face sheets, the high-order sandwich panel theory and modified couple stress theory are employed for AL-foam flexible core and face sheets, respectively. The governing nonlinear partial differential equations of dynamic stability are derived from the Hamilton’s principle and then discretized by using generalized differential quadrature method to convert them into a linear system of Mathieu–Hill equations. These formulations lead to nine partial differential equations which are coupled in axial and transverse deformations. The boundaries of the instability region are achieved by Bolotin’s method and are illustrated in the dimensionless nonlinear excitation frequency (Ω NL) and excitation frequency ratio (Ω NL/Ω L) to load amplitude plane. A parametric study is carried out to investigate the influence of some important parameters such as slenderness ratio, face sheet thickness, temperature rise, carbon nanotube volume fraction, static load factor, coefficients of Pasternak foundation, and end supports on the nonlinear dynamic instability characteristics of AL-foam core sandwich beam. The numerical results show that with temperature increasing, the nonlinear excitation frequency (Ω NL) and width of corresponding unstable zone decrease, but dynamic frequency ratio (Ω NL/Ω L) and associated unstable region increase. With an increase in the application of sandwich structures for compressible core in advanced industries such as spacecraft, high-speed aircraft, naval vessels, transportation, and automobiles, a further interest in the problem-involving dynamic instability of structures has resulted. Because of their applications, sandwich structures are frequently exposed to periodic axial compressive forces and so the dynamic instability has been a very important topic in structural dynamics and is of practical importance in different engineering industries.

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Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro beam with moving mass

Cited by 24 publications

References 39 publications

Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect

Vibration behavior of visco-elastically coupled sandwich beams with magnetorheological core and three-phase carbon nanotubes/fiber/polymer composite facesheets subjected to external magnetic field

Nonlinear high-order dynamic stability of AL-foam flexible cored sandwich beam with variable mechanical properties and carbon nanotubes-reinforced composite face sheets in thermal environment

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