Large amplitude vibrations of anisotropic cylindrical shells

Toorani, M.; Lakis, A. A.

doi:10.1016/j.compstruc.2003.07.007

Cited by 22 publications

(3 citation statements)

References 19 publications

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“…Nonlinear flexural vibration behavior of FRC cylindrical shells has received considerable attention [31][32][33][34]. However, although in a well-known reference case there seems to be a reasonable agreement, there are unresolved discrepancies between the results obtained by different authors [33].…”

Section: Introductionmentioning

confidence: 87%

Nonlinear vibration of functionally graded fiber-reinforced composite laminated cylindrical shells in hygrothermal environments

Shen

Yang

2015

Applied Mathematical Modelling

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a b s t r a c tThe effect of hygrothermal conditions on the linear and nonlinear free flexural vibration of anisotropic shear deformable laminated cylindrical shells is investigated. The cylindrical shell is made of fiber-reinforced composites (FRCs) with the reinforcement being distributed either uniformly (UD) or functionally graded (FG) of piece-wise type along the thickness of the shells. The motion equations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity. The hygrothermal effects are also included, and the material properties of FRCs are estimated through a micromechanical model and are assumed to be temperature-dependent and moisture-dependent. The equations of motion are solved by a singular perturbation technique along with a two-step perturbation approach to determine the linear and nonlinear frequencies of the FRC laminated cylindrical shells. Detailed parametric studies are carried out to investigate effects of material property gradient, the temperature change, the degree of moisture concentration, shell geometric parameter, stacking sequence, as well as the end conditions on the vibration characteristics of FRC shells with polymer matrix. The results show that the temperature/moisture variation has a moderately effect on the natural frequencies of the FRC cylindrical shells, but only has a small effect on the nonlinear to linear frequency ratios of the same shell.

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Section: Introductionmentioning

confidence: 87%

Nonlinear vibration of functionally graded fiber-reinforced composite laminated cylindrical shells in hygrothermal environments

Shen

Yang

2015

Applied Mathematical Modelling

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“…Toorani [209] and Toorani and Lakis [210] studied non linear free vibrations of composite circular cylindrical shells based on a finite element method and a shear deformation theory. In a series of papers, Jansen [211 215] used Donnell's non linear shell theory and a semi analytic method for studying non linear free and forced vibrations of orthotropic and composite shells.…”

Section: Closed Composite Shellsmentioning

confidence: 99%

Non-linear vibrations of shells: A literature review from 2003 to 2013

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

214

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International audienceThe present literature review focuses on geometrically non linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non linear vibrations of shells subjected to normal and in plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non linear vibrations of shells and panels, including (i) fluid structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non linear normal modes and meshless methods are reviewed in depth

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“…Many pioneering studies have been carried out on the vibration analysis of the elastic cylindrical shells and structural systems, and some of them can be found, for instance, in (Smith, 1968;Chung, 1981;Joseph et al, 1987;Zhang et al, 2001;Toorani and Lakis, 2004;Gokhan and Burak, 2007;Xuebin, 2008;Liu et al, 2012;Xin et al, 2011;Khalifa, 2011a;El-Kaavazi and David, 2012;Lu et al, 2013;Yuehua et al, 2013;Tomabene et al, 2014a). Unlike the circular cylindrical shells, the study of vibration behavior for the noncircular cross-section shells has been received little attention in the past decade, but only a few important studies are concerned with the vibration analysis of the shells with three-lobed, four-lobed, oval, panel and elliptical cross-section (see for example (Culberson and Boyd, 1971;Sewel and Pusey, 1971;Chen and Kempner, 1978;Koumousis and Armenakas, 1983;Yamada et al, 1984Yamada et al, , 1985Sodatos, 1999;Ganapathi et al, 2003Ganapathi et al, , 2004Tomabene and Fantuzzi, 2013;Tomabene et al 2014b;Khalifa, 2010Khalifa, , 2011bKhalifa, ,c, 2014Khalifa, , 2015 ).…”

Section: Introductionmentioning

confidence: 98%

Thermal gradient effect on the free vibration of a cardioid cross-section cylindrical shell

Ahmed

2015

Mechanics Based Design of Structures and Machines

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For the first time, a new cross-section profile and efficient method are developed for the vibration analysis of isotropic and orthotropic cylindrical shells having circumferentially varying profile of a cardioid cross-section expressed as an arbitrary function, under thermal gradient effect. The governing equations of orthotropic cylindrical shells with varying thermal gradient around its circumference are derived as a boundary-value problem and solved numerically as an initial-value problem, based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method. As a semi-analytical procedure, the trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction and also to reduce the twodimensional problem to one-dimensional one. The thermal gradient is assumed to arise due to the variation of Young's moduli and shear modulus, along the circumferential direction of the shell. The results are obtained to indicate the effects of cardioid crosssection on the natural frequencies and corresponding mode shapes in the thermal environment as well as the sensitivity of the vibration behavior to the thermal gradient ratio and the orthotropy of the shell is also investigated for different types of vibration Downloaded by [New York University] at 21:03 17 June 20152 modes. In general, close agreement between the obtained results and those of other researchers has been found.

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Large amplitude vibrations of anisotropic cylindrical shells

Cited by 22 publications

References 19 publications

Nonlinear vibration of functionally graded fiber-reinforced composite laminated cylindrical shells in hygrothermal environments

Nonlinear vibration of functionally graded fiber-reinforced composite laminated cylindrical shells in hygrothermal environments

Non-linear vibrations of shells: A literature review from 2003 to 2013

Thermal gradient effect on the free vibration of a cardioid cross-section cylindrical shell

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