A modified Fourier–Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials

Yang, Chuanlei; Jin, Guoyong; Ye, Xinmao; Liu, Zhigang

doi:10.1016/j.ijmecsci.2015.11.031

Cited by 46 publications

(17 citation statements)

References 48 publications

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“…According to the boundary conditions, the electrical and magnetic potentials distributions were expressed as a combination of cosine variations Based on the first-order shear deformation theory, the displacement field of sandwich plates in terms of in-plane (u and v) and out-of-plane w components at a point (x, y) is determined as 28 u i ðx; y; z; tÞ ¼ u i 0 ðx; y; tÞ þ zh i x ðx; y; tÞ v i ðx; y; z; tÞ ¼ v i 0 ðx; y; tÞ þ zh i y ðx; y; tÞ i ¼ s; v; c w ðx; y; z; tÞ ¼ w 0 ðx; y; tÞ (11) where u 0 , v 0 , and w 0 are the mid-plane displacements in x, y, and z directions, respectively. h x and h y show the normal rotations relative to y-and xaxes, respectively.…”

Section: Governing Equationmentioning

confidence: 99%

“…A first-order shear deformation theory combining the classical plate theory and the Hamilton's principle in variational form was employed to derive the finite element equations of motion for the sandwich plate. Yang et al 11 studied a modified Fourier-Ritz solution for vibrations of the functionally graded material (FGM) sandwich plate with the viscoelastic interlayer. The first-order shear deformation theory was used for the governing equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magneto-electro-mechanical vibration of porous functionally graded smart sandwich plates with viscoelastic core

Amanieh

Roknizadeh

Reza

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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In this paper, the vibrations of a sandwich plate with functionally graded magneto-electro-elastic (FG-MEE) face sheets and porous and viscoelastic core were investigated. Power-law rule modified by two types of porosity distributions was used to model the FG-MEE plates. The plate with even porosity distribution was considered as the FG-MEE-I model, while the one with uneven porosity distribution was labeled as the FG-MEE-II model. The normal and shear stresses were considered in the core layer, and the interlayer was modeled by the standard linear solid scheme. First-order shear deformation plate theory was used to derive the governing equation of the sandwich panel including the FG-MEE plate and viscoelastic core interaction. The governing equations were solved by the Navier method. A detailed parametric analysis was conducted to assess the effects of electric and magnetic fields, core-to-face sheet thickness ratio, and power-law index on the linear vibration characteristics of sandwich plates with functionally graded MEE face sheets. It is observed that for the FG-MEE-I model, an increase in the porosity coefficient led to a reduction in the frequency of the FG-MEE sandwich plate. On the contrary, for the FG-MEE-II model, an increment in the porosity coefficient enhanced the natural frequency.

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Section: Governing Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magneto-electro-mechanical vibration of porous functionally graded smart sandwich plates with viscoelastic core

Amanieh

Roknizadeh

Reza

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

View full text Add to dashboard Cite

show abstract

“…Joseph and Mohanty [14] designed a finite element (FE) model relied on the first-order shear deformation theory for the analysis of the free vibration of a beam with FG constraining layer and viscoelastic core. By the use of Fourier series and Rayleigh-Ritz method, a unified accurate solution based on the first-order shear deformation theory was provided by Yang et al [15] to study the vibration and damping of a FG sandwich plate with a soft or hard core. According to the refined zigzag theory, Kolahchi et al [16] dealt with the general wave propagation in a piezoelectric plate, whose core is consisted of several viscoelastic layers with temperature-dependent behaviors and reinforced by FG carbon nanotubes.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent characteristics of two-layer functionally graded plates adhesively bonded by a viscoelastic interlayer based on Kirchhoff plate theory

Yang

Liu

2020

mech

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An analytical solution is proposed to investigate the time-dependent characteristics of two-layer functionally graded plates with a viscoelastic interlayer. The elastic modulus in each graded layer varies through the thickness following an arbitrary function, and its mechanical properties are described based on the Kirchhoff theory. The Maxwell-Wiechert model is applied to simulate the viscoelastic adhesive interlayer with the neglect of memory effect. The energy equation of the system is expressed by the deformation components, which are expanded as the double trigonometric series. By virtue of variational method, the solutions of stress and deformation are determined efficiently. The comparison study indicates that the present solution matches the finite element solution well; however, the finite element method is highly time-consuming because of the fine mesh in the geometric shape and the time step. Finally, the influences of the geometry and material on the time-dependent behavior of the structure are discussed in detail.

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“…However, dynamics analyses of FGM plates are still not large 2–4 . Among them, some studies were carried out on linear dynamics of FGM plates 5–7 . On the other hand, literature on nonlinear dynamics of FGM plates is very limited.…”

Section: Introductionmentioning

confidence: 99%

A widespread internal resonance phenomenon in functionally graded material plates with longitudinal speed

Zhang

Liu

2019

Sci Rep

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A widespread internal resonance phenomenon is detected in axially moving functionally graded material (FGM) rectangular plates. The geometrical nonlinearity is taken into account with the consideration of von Kármán nonlinear geometric equations. Using d’Alembert’s principle, governing equation of the transverse motion is derived. The obtained equation is further discretized to ordinary differential equations using the Galerkin technique. The harmonic balance method is adopted to solve the above equations. Additionally, stability analysis of steady-state solutions is presented. Research shows that a one-to-one internal resonance phenomenon widely exists in a large range of constituent volume distribution in moving FGM plates. Moreover, it is found that this internal resonance phenomenon can easily happen even though the FGM plates are under extremely small external excitation or with very large damping.

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A modified Fourier–Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials

Cited by 46 publications

References 48 publications

Magneto-electro-mechanical vibration of porous functionally graded smart sandwich plates with viscoelastic core

Magneto-electro-mechanical vibration of porous functionally graded smart sandwich plates with viscoelastic core

Time-dependent characteristics of two-layer functionally graded plates adhesively bonded by a viscoelastic interlayer based on Kirchhoff plate theory

A widespread internal resonance phenomenon in functionally graded material plates with longitudinal speed

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