Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation

Pradyumna, S.; Bandyopadhyay, Jayita

doi:10.1016/j.jsv.2008.03.056

Cited by 210 publications

(91 citation statements)

References 38 publications

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“…It may be concluded that the present results exhibit close range with the above cited reference data for the maximum number of cases. Maximum exception cases in first frequency mode are observed with Pradyumna and Bandyopadhyay [17] for the values of power law exponent n = 0.0, 2.0 and 10.0. The probable reason may be due to the different model of higher order theory involved in the reference paper by Pradyumna and Bandyopadhyay [17].…”

Section: Free Vibration Analysis-validation Studymentioning

confidence: 89%

“…{q}appearing in Equation (12) is the dynamic pressure applied on the top of the shell. It is given by, q x, y,t ( ) = q 0 F(t) (17) Here, q 0 is the maximum amplitude and F(t)is a dynamic load shape function of time domain. In the present analysis F(t) is taken as unity for the case of suddenly applied load.…”

Section: Dynamic Responsementioning

confidence: 99%

“…The mode shapes of first four frequencies for different power law exponent n = 0.0, 0.2, 2.0, 10.0 and 1000 (very high value), with geometric properties a/R=0.1 and a/h=10 are investigated. The source papers considered for comparison purposes are: Neves et al [14], who adopted higher order shear deformation theory in conjunction with Carrera's unified formulation [28][29][30] and collocation radial basis techniques [31][32][33][34]; Pradyumna and Bandyobadyay [17], who presented free vibration solution using higher order shear deformation theory [25] combined with finite element formulation; and Yang and Shen [15], who carried out the vibration analysis using higher order shear deformation theory [27] and semi analytical approach. It may be concluded that the present results exhibit close range with the above cited reference data for the maximum number of cases.…”

Section: Free Vibration Analysis-validation Studymentioning

confidence: 99%

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Dynamic response of functionally graded skew shell panel

Chakrabarti

2013

Lat. Am. j. solids struct.

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The dynamic response of functionally graded skew shell is investigated using a C 0 finite element formulation. Reddy's higher order theory has been employed to perform the analysis and the volume fractions of the ceramic and metallic components are assumed to follow simple linear distribution law. The present study attempts to focus mainly on the influence of skew angle on frequency parameter and displacement of shell panel with various geometries. Comprehensive numerical results are demonstrated for cylindrical, spherical and hypar shells for different boundary conditions and skew angles.The findings obtained for functionally graded skew shell panels are new and can be used as bench mark for researchers in this field.

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Section: Free Vibration Analysis-validation Studymentioning

confidence: 89%

Section: Dynamic Responsementioning

confidence: 99%

Section: Free Vibration Analysis-validation Studymentioning

confidence: 99%

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Dynamic response of functionally graded skew shell panel

Chakrabarti

2013

Lat. Am. j. solids struct.

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“…This is especially true for linear problems (Lam et al (2002); Loy et al (2008); Matsunaga (2008); Neves et al (2013); Pradyumna and Bandyopadhyay (2008); Reddy et al (1999); Reddy (2009);Shen (2009) ;Viola (2007, 2009) ;Tornabene et al (2011);Zhu et al (2014Zhu et al ( , 2015). 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)).…”

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.

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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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“…Pradyumna S. and Bandyspadhyay J.N. received natural frequencies of FGM curved panels using highorder finite element formulation [5]. Pradhan S.C et al [6] and Loy C.T et al [7] studied vibration of FGM cylindrical shells and the effects of boundary conditions and power law indices on the natural frequencies of shells; Yang Y. and Shen H.S.…”

Section: Introductionmentioning

confidence: 99%

Non-linear vibration of functionally graded shallow spherical shells

Bich

Hoa²

2010

Vietnam J. Mech.

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Abstract. The present paper deals with the non-linear vibration of functionally graded shallow spherical shells. The properties of shell material are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents. In the derived governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. From the deformation compatibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Galerkin method and RungeKutta method are used for dynamical analysis of shells to give expressions of natural frequencies and non-linear dynamic responses. Numerical results show the essential influence of characteristics of functionally graded materials and dimension ratios on the dynamical behaviors of shells.

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Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation

Cited by 210 publications

References 38 publications

Dynamic response of functionally graded skew shell panel

Dynamic response of functionally graded skew shell panel

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

Non-linear vibration of functionally graded shallow spherical shells

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