Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature

Li, Li; Tang, Haishan; Hu, Yujin

doi:10.1016/j.compstruct.2017.10.052

Cited by 96 publications

(23 citation statements)

References 121 publications

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“…To confirm the validity of the present model, the obtained results are compared with the work of Li et al 26 for the nonlinear vibration frequencies of imperfect nanobeam based on a variety of maximum vibration amplitude ðWÞ presented in Table 2. It is observed that the results match well with those presented by Li et al 26 which demonstrate the efficient of the present model. A comparison between approximate and exact solutions for nonlinear vibration frequency at different values of normalized amplitude has been presented in Table 3.…”

Section: ∂Nmentioning

confidence: 60%

“…In this section, the procedure of obtaining governing equations for a geometrically imperfect piezo-magnetic nanobeam will be presented in the context of nonlocal and classic beam theories. To this end, displacement field of the nanobeam based on axial (u) and transverse (w) displacements at the mid-axis can be written as For considering geometric nonlinearity and imperfectness (w*), the axial strain of the beam should be written as 26,29…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In this part, by employing Galerkin's approach, the governing equations of motion for free vibration of simply supported and clamped MEE nanosize beam have been solved. The displacement functions are provided as product of non-unknown coefficients and known trigonometric functions to assure the boundary conditions at x = 0 and x=L as 18,26 w ¼…”

Section: ∂Nmentioning

confidence: 99%

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Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme

Mirjavadi

Forsat

Badnava

et al. 2020

The Journal of Strain Analysis for Engineering Design

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This article deals with analyzing nonlinear free vibrations of nonlocal two-phase piezo-magnetic beam with geometric imperfection rested on viscoelastic substrate. The two-phase piezo-magnetic material is based on a composition of piezoelectric and magnetic constituents with desirable percentages. An assumption is that the nanobeam is rested in an initial position due to geometric imperfection. In addition, the equilibrium equations of nanobeam with piezo-magnetic properties are derived utilizing Hamilton’s principle and the von Kármán geometric nonlinearity. Then, an exact solution based on the Jacobi elliptic functions has been provided to obtain nonlinear vibration frequency. It is found that nonlinear vibration behavior of the nanobeam is dependent on the magnitude of induced electric voltage, magnetic field intensity, geometric imperfection, and viscoelastic substrate parameters.

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Section: ∂Nmentioning

confidence: 60%

Section: Mathematical Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme

Mirjavadi

Forsat

Badnava

et al. 2020

The Journal of Strain Analysis for Engineering Design

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show abstract

“…Here, it is worth mentioning that both of the nonlocal and length scale parameters can be determined by means of experiments, matching the wave dispersion of atomic lattice dynamics. 65,66 Once the nonlocal kernel functions 0 ðx, x 0 , e 0 aÞ and 1 ðx, x 0 , e 1 aÞ satisfy the developed conditions, the constitutive relation of NSGT can be expressed as follows…”

Section: Kinematic Relationsmentioning

confidence: 99%

Wave propagation analysis of magnetostrictive sandwich composite nanoplates via nonlocal strain gradient theory

Ebrahimi

Dabbagh

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, the survey of the wave dispersion behaviors of sandwich composite nanoplates is carried out by considering the magnetostriction phenomenon. The nanoplate is assumed to be made up of a central magnetostrictive core in addition to two composite face sheets. The scale influences are covered based on the nonlocal strain gradient theory. Moreover, the equations of plate motion are derived according to the classical plate theory. Afterward, the magnetization effects are considered by introducing a feedback control system. Then, Hamilton’s principle is introduced to obtain the Euler–Lagrange equations of the magnetostrictive sandwich composite nanoplate. Also, by relating the achieved equations with those of the nonlocal strain gradient theory, the nonlocal governing equations of magnetostrictive sandwich composite nanoplate are developed. The wave frequency and phase velocity values are computed by the application of an analytical solution. Finally, the effects of participant coefficients are illustrated separately through certain figures.

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“…47 The NSGT was also chosen for analyzing the size-dependent mechanical behavior of various nanostructures, e.g. buckling, 48,49 vibration, 50–53 and wave propagation. 54–57…”

Section: Introductionmentioning

confidence: 99%

Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field

Karami

Shahsavari

Karami

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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Flexural and longitudinal wave behaviors of nanobeams made of nanoporous-graded materials while surrounded by Winkler-Pasternak foundation, subjected to the longitudinal magnetic field and exposed to the hygrothermal environment are studied analytically. To this end, the governing equation derived by Euler–Bernoulli beam theory in conjunction with the nonlocal strain gradient theory is defined by employing Hamilton’s principle. By adopting an analytic model, the flexural and longitudinal dispersion relations between phase velocity and wave number are derived. The reliability of the present method is confirmed by comparing the obtained results with those stored in the literature. Finally, the effects of the power-law index, porosity volume fraction, nonlocal and material characteristic parameters, uniform temperature and moisture rise, elastic foundation parameters, magnetic field intensity, and wave number are also investigated in detail. It is found that the small-scale parameters are more influential in higher wave numbers where the wavelength is close to the length scale of nanostructures. However, foundation parameters, porosity volume fraction, and longitudinal magnetic field are more influential in lower wave numbers.

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Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature

Cited by 96 publications

References 121 publications

Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme

Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme

Wave propagation analysis of magnetostrictive sandwich composite nanoplates via nonlocal strain gradient theory

Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field

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