Nonlinear vibrations of functionally graded doubly curved shallow shells

Alijani, Farbod; Amabili, Marco; Karagiozis, Kostas; Bakhtiari-Nejad, Firooz

doi:10.1016/j.jsv.2010.10.003

Cited by 164 publications

(47 citation statements)

References 19 publications

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“…In general, it should be noted that the classical theory, in most of cases, overestimates the fundamental frequencies compared with the refined theory. [Alijani et al (2011b)] (FSDT) [Chorfi and Houmat (2010)] (HSDT) [Matsunaga (2008) …”

Section: Results Validationmentioning

confidence: 99%

“…However, in the last decade, nonlinear free and forced vibrations of the FG shells have been extensively studied as well (Reddy et al (1999); Reddy (2009);Shen (2009); Amabili (2008); Alijani et al (2011a,b); Bich et al (2012); Chorfi and Houmat (2010); Sundararajan et al (2005); Woo et al (2006); Xiang et al (2015); Zhao and Liew (2009)). A complete survey on linear and nonlinear vibrations of FG plates and shells can be found in the following references (Shen (2009) ;Tornabene et al (2011);Zhu et al (2014); Amabili (2008); Alijani et al (2011b)). Note that in the aforementioned papers, nonlinear vibrations of simply supported or clamped FG structures of rectangular, skew or circle planforms have been analyzed by different numerical methods such as Finite Element Method (FEM) [Lam et al (2002); Loy et al (2008); Matsunaga (2008); Reddy et al (1999); Reddy (2009);Shen (2009) ;Bich et al (2012)], Differential Quadrature Method Viola (2007, 2009) ;Tornabene et al (2011)], modified Fourier-Ritz Approach [Zhu et al (2014[Zhu et al ( , 2015], etc.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells of a Complex Shape

Awrejcewicz

Kurpa

Shmatko

2017

Lat. Am. j. solids struct.

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Geometrically nonlinear vibrations of functionally graded shallow shells of complex planform are studied. The paper deals with a power-law distribution of the volume fraction of ceramics and metal through the thickness. The analysis is performed with the use of the R-functions theory and variational Ritz method. Moreover, the Bubnov-Galerkin and the Runge-Kutta methods are employed. A novel approach of discretization of the equation of motion with respect to time is proposed. According to the developed approach, the eigenfunctions of the linear vibration problem and some auxiliary functions are appropriately matched to fit unknown functions of the input nonlinear problem. Application of the R-functions theory on every step has allowed the extension of the proposed approach to study shallow shells with an arbitrary shape and different kinds of boundary conditions. Numerical realization of the proposed method is performed only for one-mode approximation with respect to time. Simultaneously, the developed method is validated by investigating test problems for shallow shells with rectangular and elliptical planforms, and then applied to new kinds of dynamic problems for shallow shells having complex planforms.

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Section: Results Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells of a Complex Shape

Awrejcewicz

Kurpa

Shmatko

2017

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

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“…Three types of simply supported shallow shells with positive, zero, and negative Gaussian curvature were considered. Alijani et al [31] investigated the nonlinear forced vibrations of simply supported FG doubly curved shallow shells based on Donnell's nonlinear shallow shell theory and the Galerkin method. Su et al [32] presented a unified solution for vibration analysis of FG cylindrical, conical shells and annular plates with general boundary conditions by applying the FSDT and Rayleigh-Ritz procedure.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Shi

Zha

Zhang

et al. 2017

Shock and Vibration

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The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and RayleighRitz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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“…Rahimia et al (2011) studied the vibration responses of cylindrical FG shell panel with intermediate ring supports using Sanders' thin shell theory. Alijani et al (2011a) investigated the nonlinear forced vibration behaviour of the simply-supported FG curved shallow shells using Donnell's nonlinear shallow shell theory. Alijani et al (2011b) analysed the nonlinear vibration responses of the FG shell panel using the HSDT kinematics including the temperature effect.…”

Section: Introductionmentioning

confidence: 99%

Free vibration responses of temperature dependent functionally graded curved panels under thermal environment

Kar

Panda

2015

Lat. Am. j. solids struct.

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Free vibration responses of shear deformable functionally graded single/doubly curved panels under uniform, linear and nonlinear temperature fields are investigated in the present article. The micromechanical material model of functionally graded material is computed using Voigt model in conjunction with the power-law distribution to achieve the continuous gradation. The material properties are assumed to be the function of temperatures. The mid-plane kinematics of panel geometry is derived using the higher order shear deformation theory. The governing equation of the vibrated panel is obtained using Hamilton's principle. The desired solutions of free vibrated functionally graded shells are computed numerically using the suitable finite element steps. The convergence behaviour of the numerical results has been checked and validated by comparing the responses with that to available published literatura. The applicability of the proposed model has been highlighted by solving various numerical examples for different material and geometrical parameters and temperature fields.

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Nonlinear vibrations of functionally graded doubly curved shallow shells

Cited by 164 publications

References 19 publications

Analysis of Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells of a Complex Shape

Analysis of Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells of a Complex Shape

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Free vibration responses of temperature dependent functionally graded curved panels under thermal environment

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