A Nonlinear Theory for the Bending, Buckling, and Vibrations of Conical Shells

Bendavid, Dror; Mayers, J.

doi:10.21236/ad0873255

Cited by 2 publications

(7 citation statements)

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“…Infinite single shells. The problem of blood flow has been addressed [17][18][19]. Dispersion relations for axisymmetric flexural (Young) wave propagation through fluid-filled, circular cylindrical, flexible tubes of infinite extent were studied.…”

Section: Cylindrical Shellsmentioning

confidence: 99%

“…Dispersion in an inviscid, incompressible fluid inside an elastic thin-walled tube has been treated approximately [18]. The author's references are not current and do not include any important recent papers on this subject.…”

Section: Cylindrical Shellsmentioning

confidence: 99%

“…On the basis of Love's assumptions of first approximation [12,13], the equations of motion of vibration for a shell element were derived either by using Newton's second law of motion by applying d'Alembert's principle to the equations of equilibrium (14)(15)(16), or by applying the Hamilton principle through the variational method [17,18]. The last approach provides a set nf geometric as well as natural boundary conditions.…”

Section: Formulationsmentioning

confidence: 99%

“…They can be identically satisfied by introducing the Airy stress function $ for the slresi?« A compatibility equation and the equation of motion in the / direction form the two coupled Donnell-type equations for the two unknown functions 0 and w [24]. A set of nonlinear Donnell-type equations has also been derived [18].…”

Section: Formulationsmentioning

confidence: 99%

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Svic Notes

1985

The Shock and Vibration Digest

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The introduction of the mini-computer into the dynamics test laboratory has made it possible to use several forms of multi-frequency excitation to speed up and simplify modal testing. These techniques have been described in the recent literature which has revealed that some of these forms of excitation are now used routinely in modal tests. A few of the earlier classical modal testing techniques have been upgraded and they are still in use. Therefore the test engineer has a wider choice of testing techniques and this could lead to difficulties in selecting the proper test method if several methods appear to be suitable. Thus published guidance for selecting proper modal test methods is needed. This information need might be met in any of the following ways. Modal testing techniques have matured to the point where a review of all of the available methods might be published. It should include, but not be limited to, a description of the various methods, their advantages and limitations and their suitability for modal tests of various types of hardware. More published comparisons of the results of modal te^.s, using a number of different test methods, would be useful, in addition to the obvious comparison of the modal parameters and the ability to isolate all significant modes, other comparisons should be made. These should include the ease of performing the test, the overall cost of testing, instrumentation requirements and the complexity of the data processing requirements. In 1976 a survey of modal testing practices was conducted. A number of factors were examined, such as the type of excitation, instrumentation, test article boundary and support conditions and many more. It is time to undertake a similar survey to see what changes in modal testing practices have occurred. Any or all of the above steps would be helpful in defining the state of the art of modal testing, but more importantly, they would provide guidance for selecting a testing technique, or techniques, that would be the most suitable for the job. This is important because use of the wrong test method could lead to confusing and/or meaningless results. R.H.V. f (^> crt. i£ :2i LITERATURE REVIEW:-' Vibration lltoratur« The monthly Literature Review, a subjective critique and summary of the literature, consists of two to four review articles each month, 3,000 to 4,000 words in length. The purpose of this section is to present a "digest" of literature over a period of three years. Planned by the Technical Editor, this section provides the DIGEST reader with up-to-date insights into current technology in more than 150 topic areas. Review articles inlcude technical information from articles, reports, and unpublished proceedings. Each article also contains a minor tutorial of the technical area under discussion, a survey and evaluation of the new literature, and recommendations. Review articles are written by experts in the shock and vibration field. This issue of the DIGEST contains an article about vibrations of conical shells. Professor C.H. Chang of t...

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Section: Cylindrical Shellsmentioning

confidence: 99%

Section: Cylindrical Shellsmentioning

confidence: 99%

Section: Formulationsmentioning

confidence: 99%

Section: Formulationsmentioning

confidence: 99%

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Svic Notes

1985

The Shock and Vibration Digest

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“…Sun et al [2] studied the dynamic response of conical and cylindrical shells under ramp and sinusoidal temperature loads using Donnell's nonlinear shallow shell theory. Bendavid et al [3] developed a nonlinear theory for bending, buckling and vibrations of conical shells based on Sander's nonlinear theory and proposed a variation of generalized coordinates method to predict the shell's response. Kanaka Raju et al studied the large -amplitude asymmetric vibrations of shells of revolutions employing Sander's nonlinear kinematics to obtain finite element's stiffness matrix.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories

Bakhtiari

Lakis

Kerboua

2019

International Journal of Nonlinear Sciences and Numerical Simulation

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Nonlinear free vibration of truncated conical shells has been investigated for three different shell theories; Donnell, Sanders and Nemeth to investigate the effect of their simplifying assumptions. The displacement field of a finite element model that was obtained from the exact solution of equilibrium equations of Sander’s improved first-approximation theory is used to define the nonlinear strain energy of conical shells. Employing generalized coordinates method the equations of motion are derived and subsequently the amplitude equation of nonlinear vibration of conical shells was developed. The amplitude equation is solved for multiple cases of isotropic materials. Linear and nonlinear free vibration results are validated against the existing studies in scientific literature and demonstrate good accordance. The validated model is used to investigate effects of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions for the nonlinear vibration of conical shells.

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A Nonlinear Theory for the Bending, Buckling, and Vibrations of Conical Shells

Cited by 2 publications

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Svic Notes

Svic Notes

Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories

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