Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory

Vuong, Pham Minh; Duc, Nguyen Dinh

doi:10.1007/s10999-019-09473-x

Cited by 35 publications

(10 citation statements)

References 32 publications

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“…Saffari et al [14] presented dynamic stability of FG Nanobeam subjected to thermal and axial loading according to theory of nonlocal Timoshenko beam. Meksi et al [15] A new shear deformation plate model was investigated to demonstrate the buckling, vibration, and bending analyzes of FGM sandwich plates by Meksi and et al Vuong and Duc [16] investigated dynamic analysis and nonlinear vibration response of moderately functionally graded thick toroidal shell segments embedded on Pasternak medium. Tian et al [17] presented free vibration response of rotating porosities FGM beams with double tapered cross-section solving by a semi-analytical model.…”

Section: Introductionmentioning

confidence: 99%

Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories

et al. 2021

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The dynamic stability response of a micro sandwich beam with leptadenia pyrotechnica rheological elastomer (LPRE) core is studied. The top and bottom layers respectively are assumed as piezoelectric reinforced with carbon nanotubes (CNTs) and porous functionally graded materials (FGM). The core and top layers are affected by magnetic and electric fields for the magnetic and piezoelectric characteristics of the layers, respectively. The Halpin-Tsai micromechanics theory for obtaining the effective material properties of the nanocomposite layer is utilized. On the basis of Kelvin-Voigt model, the structural damping of the smart micro beam is assumed. The microstructure is located on the viscoelastic model which is simulated using Visco-Pasternak platform. The size effects are assumed according to the theory of strain gradient including three-length scale constants. The various theories of first-order shear deformation beam theory (FSDBT), third-order shear deformation beam theory (TSDBT), parabolic shear deformation beam theory (PSDBT), and exponential shear deformation beam theory (ESDBT) are utilized for driving the governing equations according to the Hamilton's principle. The motion final relations are solved by the differential quadrature method (DQM) for presenting the dynamic buckling area. The effects of different components such as volume percentage and distribution of GPLs, porosities, magnetic field of LPRE, applied voltage, FG index, structural damping, and geometric components of the micro sandwich beam on the dynamic stability reign (DIR) of the system are shown. The results with other researcher papers are compared. The results show that the DIR increases by applying a magnetic field to the LPRE layer.

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Section: Introductionmentioning

confidence: 99%

Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories

et al. 2021

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“…With the aid of higher-order shear theory, Wang and Shen (2011) and Alijani and Amabili (2013) examined the linear and nonlinear vibration behavior of sandwich plates. Using the Reddy’s third shear theory, Vuong and Duc (2020), Duc et al (2015a, 2015b), and Khoa et al (2019) studied the nonlinear dynamics of functionally graded toroidal shells, circular cylindrical shells, and the nonlinear buckling and postbuckling of the imperfect FGM circular cylindrical shells with piezoelectric actuators, respectively. Chan et al (2019) applied the shear theory to study the vibration and nonlinear dynamics of FGM truncated conical panel attached by piezoelectric actuators.…”

Section: Introductionmentioning

confidence: 99%

“…Khayal (2017) reviewed the common imperfection of laminated plates and shells caused by fabrication. Duc and Cong (2015), Duc and Thang (2015), Duc and Quan (2015) and Duc et al (2020) studied the nonlinear dynamics of the imperfect FGM plates, double curved shallow shells, and circular cylindrical shells under various conditions, which can help researchers obtain knowledge of imperfect FGM structures. Furthermore, they also reported the research studies of dynamic and static problems of the FGM cylindrical panels with the oblique stiffeners.…”

Section: Introductionmentioning

confidence: 99%

Natural vibration of imperfect sandwich plates considering the effects of transverse stretching

Yang

Zhang

et al. 2021

Journal of Vibration and Control

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In this article, the natural vibration investigation of a functionally graded material sandwich plate with initial geometrical imperfection of the exponential function is conducted. Two face sheets of the sandwich plate are composited by functionally graded material. Their material coefficients are affected by temperature and vary in the direction of thickness following the power law. The core layer is only the metal. With the aid of Reddy’s displacement fields, a quasi-three-dimensional model is used, in which the effects of transverse stretching on natural vibration are considered. The natural frequencies and model shapes of the system are calculated on the basis of Rayleigh–Ritz method and Chebyshev polynomials. A comparison of these results with those of the existing three-dimensional theory results shows the validity and computability of present method. The influences of various parameters on the natural frequencies are researched in detail.

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“…[25] presented an analytical solution for the free vibrations of simply supported (SS) beams with arbitrarily and continuously varying thickness based on the two‐dimensional elasticity theory and employing the Fourier sinusoidal series expansion for small deflection assumption. Vuong and Duc [39] studied the nonlinear vibrations and dynamic response of FG moderately thick toroidal shell segments resting on Pasternak type elastic foundation by using Runge–Kutta method. Xie et al.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear vibrations of variable cross‐section beams using shear deformation theory

Sohani

Eipakchi

2021

Z Angew Math Mech

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In the present paper, the governing equations of a vibratory beam with moderately large deflection and arbitrary cross‐section are derived by using the first‐order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the axial loads. The kinematic of the problem is according to the von‐Kármán strain‐displacement relations and the Hooke law is used as the constitutive equations. The partial differential governing equations describing the axial and transverse vibrations of homogeneous beams contain four coupled nonlinear equations with variable coefficients which are derived employing Hamilton's principle. The Galerkin method in conjunction with the perturbation technique is applied to obtain the linear natural frequencies. A parametric study is performed and the effects of different thickness functions such as linear, polynomial and trigonometric on the results are investigated. The non‐linear frequencies which contain the corrections on the linear frequencies are calculated. The corrected parts of the non‐linear frequencies are functions of the axial as well as the transverse amplitudes of the vibrations. The influences of the axial load and aspect ratio on the linear and non‐linear frequencies are studied too. To confirm the reliability of the vibration analysis carried out in the present paper, the analytical results are checked with the corresponding numerical results obtained from the finite element analysis. The numerical and analytical results are in a good agreement.

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Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory

Cited by 35 publications

References 32 publications

Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories

Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories

Natural vibration of imperfect sandwich plates considering the effects of transverse stretching

Linear and nonlinear vibrations of variable cross‐section beams using shear deformation theory

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