Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM

Malekzadeh, P.

doi:10.1016/j.tws.2007.08.016

Cited by 40 publications

(14 citation statements)

References 31 publications

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“…where N is the grid points along , and C ðkÞ jm represent the Lagrange interpolation polynomial and it's kth derivative, that can be found in Ref. 42. Imposing the C-C boundary conditions into equations ( 19)-( 24) leads the following constitutive matrix equation as:…”

Section: Solution Methodsmentioning

confidence: 99%

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Arani

Kolahchi

2013

Proceedings of the Institution of Mechanical Engineers, Part C:

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Nonlinear vibration and instability of embedded double-walled carbon nanocones subjected to axial load are investigated in this article based on Eringen's nonlocal theory and Timoshenko beam model. The elastic medium is simulated as Pasternak foundation and the van der Waals forces between the inner and the outer layers of double-walled carbon nanocones are taken into account. Using von Kármán geometric nonlinearity, energy method and Hamilton’s principle, the nonlocal nonlinear motion equations are obtained. The differential quadrature method is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency and critical fluid velocity of viscous-fluid-conveying double-walled carbon nanocones. A detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, thickness-to-length ratio, temperature change, apex angles, elastic medium and van der Waals forces on the dimensionless frequency and critical buckling load of double-walled carbon nanocones. The results show that the small-size effect on the nonlinear frequency is significant and cannot be neglected; also, the nonlinear frequency and critical buckling load decrease with increasing the cone apex-angle.

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Section: Solution Methodsmentioning

confidence: 99%

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Arani

Kolahchi

2013

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…After that, great attention was given to the nonlinear vibration behavior of the structures. Mindlin plate theory was used by Malekzadeh 32 to analyze nonlinear free vibration of the plates. Furthermore, in another work, considering small-scale effect, Setoodeh et al 33 analyzed the small-scale effect on the characteristics of the nonlinear vibration of orthotropic single-layered graphene sheet (SLGS).…”

Section: Introductionmentioning

confidence: 99%

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation

Ebrahimi

Hosseini

2019

The Journal of Strain Analysis for Engineering Design

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Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton’s principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures.

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“…To the author's best knowledge, in the previous works only the mechanical vibrations of FGM circular plates are investigated and there have been few researches dealing with the free vibration behavior of moderately thick circular plates, especially the effects of thermal environment are not considered. The few researches are Malekzadeh [21], who studied the free vibration characteristic of tapered Mindlin plates using DQM. Malekzadeh et al [22] presented the vibration analysis of FGM thick annular plates subjected to thermal environment based on 3D elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Shooting method for free vibration of FGM Reissner-Mindlin circular plates resting on elastic foundation in thermal environments

Li¹,

Weidi²,

Zhu³

2017

J. vibroeng.

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This paper presents a free vibration analysis of functionally graded Reissner-Mindlin circular plates with various supported boundaries in thermal environments. A FGM consisting of metal and ceramic was considered in the study. Based on the geometric equation, physical equation and equilibrium equation of thick plate, taking into account the transverse shearing deformation, the free vibration equation of the axisymmetric FGM moderately thick circular plates was derived in terms of the middle surface angles of rotation and lateral displacement. The material properties of the plate were assumed to vary continuously in the thickness direction according a power law. By using shooting method to solve the coupled ordinary differential equations with different boundary conditions, the natural frequencies of FGM thick circular plates were obtained numerically. The effects of material gradient property, thickness ratio and boundary conditions on the natural frequencies were discussed in detail.

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Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM

Cited by 40 publications

References 31 publications

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation

Shooting method for free vibration of FGM Reissner-Mindlin circular plates resting on elastic foundation in thermal environments

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