Elastostatik und Elastokinetik in Matrizenschreibweise

Uhrig, Richard

doi:10.1007/978-3-662-11636-4

Cited by 59 publications

(12 citation statements)

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“…The relations between strains and deflections for the cylindrical shells are taken from Novozhilov (1964) and Uhrig (1973) as follows: and xs D are the extensional rigidities, and on considering the thermal gradient, using equation (5), they take the forms:…”

Section: Cylindrical Shell Basic Equationsmentioning

confidence: 99%

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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Section: Cylindrical Shell Basic Equationsmentioning

confidence: 99%

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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“…The relations between strains and deflections for the cylindrical shells used here are taken from [24] and [25] as follows:…”

Section: Basic Governing Equationsmentioning

confidence: 99%

“…As known to the researchers that the situation is different if the variable thickness shell is rested on Pasternak elastic foundation regardless the presence/absence of the Winkler elastic foundation, and Eqs. (25) and (26) give a set of eigen frequencies and the lowest values for the radial vibration modes and the biggest values for the axial modes whereas the middle for the torsional modes. Hereby, Fig.…”

Section: Vibration Analysismentioning

confidence: 99%

“…To obtain the (SS, AA) vibration modes corresponding to a particular frequency parameter of the shell, we substitute by λ into Eqs. (25) and (26) and using Gaussian elimination technique to obtain the state vector at any point of the cross-section. It is found that the foundation modulus primarily affects on the eigen frequency modes, whereas the ones has less influences on the mode shapes of vibration.…”

Section: Vibration Mode Shapesmentioning

confidence: 99%

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Winkler and Pasternak foundations effect on the free vibration of an orthotropic oval cylindrical shell with variable thickness

Ahmed

2014

Z. Angew. Math. Mech.

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In this paper, based on the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method, the vibration behavior of an elastic oval cylindrical shell with parabolically varying thickness along of its circumference resting on the Winkler‐Pasternak foundations is investigated. The theoretical analysis of the governing equations of the shell is formulated to overcome the mathematical difficulties of mode coupling of variable curvature and thickness of shell. Using the transfer matrix of the shell, the vibration equations based on the Winkler‐Pasternak foundations are written in a matrix differential equation of first order in the circumferential coordinate and solved numerically. The proposed model is applied to get the vibration frequencies and the corresponding mode shapes of the symmetrical and antisymmetrical vibration modes. The sensitivity of the vibration characteristics and bending deformations to the Winkler‐Pasternak foundations moduli, thickness variation, ovality and orthotropy of the shell is studied for different type‐modes of vibration.

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“…where The relations between strains and deflections for the cylindrical shells used here are taken from [29] as follows: …”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

Vibration and Buckling Approximation of an Axially Loaded Cylindrical Shell with a Three Lobed Cross Section Having Varying Thickness

Ahmed¹

2011

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On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of crosssection and radius variation at lobed corners of the shell on the natural frequencies, mode shapes and critical loads are examined.

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Elastostatik und Elastokinetik in Matrizenschreibweise

Cited by 59 publications

References 0 publications

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

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

Winkler and Pasternak foundations effect on the free vibration of an orthotropic oval cylindrical shell with variable thickness

Vibration and Buckling Approximation of an Axially Loaded Cylindrical Shell with a Three Lobed Cross Section Having Varying Thickness

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