Nonlinear vibrations of circular cylindrical panels

Amabili, Marco; Pellegrini, M.

doi:10.1016/b978-008044046-0.50014-2

Cited by 5 publications

(11 citation statements)

References 4 publications

(9 reference statements)

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“…As expansões modais para os campos de deslocamentos de painéis cilíndricos dadas em Alijani e Amabili (2012) e Amabili (2004)…”

Section: Sistema De Equações Não-linearesunclassified

Análise estática não-linear de cascas conoidais

Silva¹,

Soares²,

Morais³

2017

Proceedings of the XXXVIII Iberian Latin American Congress on Computational Methods in Engineering

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Com muita gratidão, agradeço àqueles que me apoiaram, ajudaram e acompanharam tornando possível a produção desta dissertação. Primeiramente a Deus, por sua graça e bondade eterna na minha vida, guiando-me em cada passo e dando-me a força necessária para seguir o caminho. Aos meus queridos familiares, um agradecimento especial aos meus pais Ivan e Fátima, por me amarem e fazerem o possível para que meus sonhos se realizem sem nunca esperar qualquer vantagem para si e nem pedirem nada em troca. Por acreditarem e incentivarem o meu desejo de obter mais esta conquista dou-lhes meu mais profundo respeito, amor e consideração. Às minhas irmãs, Franciellen e Juliana, por me encorajarem e incentivarem, desejando-me sempre sucesso mesmo nas mais difíceis decisões. Ao meu amado, Eduardo, que apareceu em minha vida para me fazer feliz e estando sempre ao meu lado nas dificuldades com toda sua paciência, amor e amizade, se tornou parte integrante do resto de minha vida. À Madalena por seu apoio, dedicação e, principalmente, ter dado à luz a meu amado. Não posso deixar de citar os professores do mestrado, peço-lhes licença para chamá-los pelo primeiro nome, Renata, Frederico, Sylvia, Daniel, Marcos, Júlio e Zenón, pois se não fosse por eles este mestrado não seria possível. Aos professores orientadores Renata e Frederico, pela sabedoria, paciência, prontidão e dedicação ao longo do desenvolvimento desta dissertação. Agradeço ao Programa de Pós Graduação em Geotecnia, Estruturas e Construção Civil da Universidade Federal de Goiás e também à CAPES pelo apoio financeiro.

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“…As expansões modais para os campos de deslocamentos de painéis cilíndricos dadas em Alijani e Amabili (2012) e Amabili (2004)…”

Section: Sistema De Equações Não-linearesunclassified

Análise estática não-linear de cascas conoidais

Silva¹,

Soares²,

Morais³

2017

Proceedings of the XXXVIII Iberian Latin American Congress on Computational Methods in Engineering

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“…More refined classical non-linear shell theories have been applied to study large-amplitude vibrations of cylindrical shells in Refs. [1,4,[14][15][16][17][18][19][20]. In particular, the Sanders-Koiter (also referred as Sanders), the Flügge-Lur'e-Byrne, the Novozhilov and the Donnell non-linear shell theories retaining in-plane inertia have been used.…”

Section: Introductionmentioning

confidence: 99%

“…Another important refinement in studies on non-linear dynamics of shells is achieved increasing the number of modes (i.e. degrees of freedom (dofs)) retained in the approximating functions [10,[17][18][19][20][21][22]. Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [19,20] present a comprehensive discussion on the importance of introducing the multimode expansions of shell displacements into analysis.…”

Section: Introductionmentioning

confidence: 99%

“…In general, the majority of the available studies address the nonlinear dynamics of circular cylindrical panels or double curved shallow shells with simple geometric shapes; e.g. with a rectangular base [5][6][7][8][9][10][11][12][13][17][18][19][20]22]. The complex geometry of the shell significantly increases the numerical difficulty of the problem.…”

Section: Introductionmentioning

confidence: 99%

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Non-linear vibrations of shallow circular cylindrical panels with complex geometry. Meshless discretization with the R-functions method

Pilgun

Amabili

2012

International Journal of Non-Linear Mechanics

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Geometrically non-linear forced vibrations of a shallow circular cylindrical panel with a complex shape, clamped at the edges and subjected to a radial harmonic excitation in the spectral neighborhood of the fundamental mode, are investigated. Both Donnell and the Sanders-Koiter non-linear shell theories retaining in-plane inertia are used to calculate the elastic strain energy. The discrete model of the non-linear vibrations is build using the meshfree technique based on classic approximate functions and the R-function theory, which allows for constructing the sequences of admissible functions that satisfy given boundary conditions in domains with complex geometries; Chebyshev orthogonal polynomials are used to expand shell displacements. A two-step approach is implemented in order to solve the problem: first a linear analysis is conducted to identify natural frequencies and corresponding natural modes to be used in the second step as a basis for expanding the non-linear displacements. Lagrange approach is applied to obtain a system of ordinary differential equations on both steps. Different multimodal expansions, having from 15 up to 35 generalized coordinates associated with natural modes, are used to study the convergence of the solution. The pseudo-arclength continuation method and bifurcation analysis are applied to study non-linear equations of motion. Numerical responses are obtained in the spectral neighborhood of the lowest natural frequency; results are compared to those available in the literature. Internal resonances are also detected and discussed.

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Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures

Touzé

Thomas

Huberdeau

2004

Computers & Structures

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Non-linear normal modes (NNMs) are used in order to derive accurate reduced-order models for large amplitude vibrations of structural systems displaying geometrical nonlinearities. This is achieved through real normal form theory, recovering the definition of a NNM as an invariant manifold in phase space, and allowing definition of new coordinates non-linearly related to the initial, modal ones. Two examples are studied: a linear beam resting on a non-linear elastic foundation, and a non-linear clamped-clamped beam.Throughout these examples, the main features of the NNM formulation will be illustrated: prediction of the correct trend of non-linearity for the amplitude-frequency relationship, as well as amplitude-dependent mode shapes. Comparisons betwen different models -using linear and non-linear modes, different number of degrees of freedom, increasing accuracy in the asymptotic developments-are also provided, in order to quantify the gain in using NNMs instead of linear modes.

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Nonlinear vibrations of circular cylindrical panels

Cited by 5 publications

References 4 publications

Análise estática não-linear de cascas conoidais

Análise estática não-linear de cascas conoidais

Non-linear vibrations of shallow circular cylindrical panels with complex geometry. Meshless discretization with the R-functions method

Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures

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