Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions

Kurylov, Ye.; Amabili, Marco

doi:10.1016/j.jsv.2009.10.038

Cited by 55 publications

(17 citation statements)

References 28 publications

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“…Kurylov and Amabili [73] compared the large amplitude response of isotropic shells obtained using Chebyshev polynomials, power polynomials and trigonometric functions for simply supported and clamped boundary conditions. The Sanders Koiter non linear shell theory was used and it was found that trigonometric functions are very efficient for simply supported boundary conditions while they require a large number of degrees of freedom for other boundary conditions, thereby decreasing the computational efficiency.…”

Section: Free and Forced Vibrations Of Shells Due To Radial Excitationmentioning

confidence: 99%

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

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

211

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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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Section: Free and Forced Vibrations Of Shells Due To Radial Excitationmentioning

confidence: 99%

“…The only publications available since 2003 are those by Kurilov and Mikhlin [135] (even if the spelling of both name and surname is different, the first author is the same author of Refs. [73,74] ) and Jansen [136]. Donnell's non linear shallow shell theory was used in both works.…”

Section: Fluid Structure Interaction For Shells Subjected To Flowing mentioning

confidence: 99%

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

Alijani

Amabili

2014

International Journal of Non-Linear Mechanics

211

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“…In Fig. 8, mode shapes are reported from the finite element analysis for { } ( , ) (1,1), (2,4), (3,3) m n = modes. Overall, the validity of the exact method was approved with comparison to experimental, numerical and theoretical results.…”

Section: Validation Of the Exact Analysismentioning

confidence: 99%

“…A comprehensive summary and discussion of shell theories, including natural frequencies and mode shape identification, has been done by Liessa [1] in 1973. More recently, adopting a non-linear point of view, Amabili and Paidoussis [2], Amabili [3] and Kurylov and Amabili [4] have presented noteworthy reviews on cylindrical shell vibration. Many researchers such as Flugge [5] have followed the pioneering work of Love [6], using his first approximation theory.…”

Section: Introductionmentioning

confidence: 99%

Exact analysis of resonance frequency and mode shapes of isotropic and laminated composite cylindrical shells; Part I: analytical studies

Oliazadeh

Farshidianfar

2013

J Mech Sci Technol

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In order to study the free vibration of simply supported circular cylindrical shells, an exact analytical procedure is developed and discussed in detail. Part I presents a general approach for exact analysis of natural frequencies and mode shapes of circular cylindrical shells. The validity of the exact technique is verified using four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter and 4) Donnell. The exact procedure is compared favorably with experimental results and those obtained using a numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The accuracy of the resonance frequencies obtained using the approximate method are also investigated by comparing results with those of the exact analysis. Part II presents effects of different parameters on mode shapes and natural frequencies of circular cylindrical shells.

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“…A comprehensive summary and discussion of shell theories including natural frequencies and mode shape informat ion has been done by Liessa [1] in 1973. More recently, Amabili and Paidoussis [2], A mabili [3] and Kurylov and A mabili [4] have presented noteworthy reviews with a non-linear point of v iew. Many investigations followed the p ioneering work of Love [5] using his first approximation theory, such as Flugge [6].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Circular Cylindrical Shells: Comparison of Different Shell Theories

Farshidianfar¹,

Oliazadeh²

2012

MECHANICS

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In order to study the free vib ration of simply supported circular cy lindrical shells, a semi-analytical p rocedure is discussed in detail. In this technique, beam function is used as an approximat ion for simp ly supported boundary conditions. A literature review reveals that beam functions are used extensively in predicting natural frequencies of shells. Since this method does not involve with boundary condition equations, there is no need to deal with intense calculations. Hence, it is important to check the accuracy of this approximate technique. So this method was applied to ten different shell theories: 1) Donnell-Mushtari, 2) Love-Timoshenko, 3) Arno ld-Warburton, 4) Houghton-Johns, 5) Flugge-Byrne-Lur'ye, 6) Reissner-Naghdi-Berry, 7) Sanders, 8) Vlasov, 9) Kennard-Simp lified and 10) Soedel. The appro ximate procedure was compared favorably with experimental results. Finally, variations and influences of length, radius and thickness were studied on amplitude ratios.

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Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions

Cited by 55 publications

References 28 publications

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

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

Exact analysis of resonance frequency and mode shapes of isotropic and laminated composite cylindrical shells; Part I: analytical studies

Free Vibration Analysis of Circular Cylindrical Shells: Comparison of Different Shell Theories

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