A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach

Amabili, Marco

doi:10.1016/s0022-460x(02)01385-8

Cited by 172 publications

(96 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where G 12 , G 13 and G 23 are the shear moduli in the 1-2, 1-3 and 2-3 directions, respectively, and the superscript (k) refers to the kth layer within a laminate. Equation (2.6) is obtained (i) under the transverse isotropy assumption with respect to planes orthogonal to axis 1, i.e.…”

Section: First Step: Natural Modesmentioning

confidence: 99%

“…Equation (2.6) is obtained (i) under the transverse isotropy assumption with respect to planes orthogonal to axis 1, i.e. assuming fibres in the direction parallel to axis 1, so that E 2 = E 3 , G 12 = G 13 and ν 12 = ν 13 , and (ii) by solving the constitutive equations for ε 33 as a function of ε 11 and ε 22 and then eliminating it. Equation (2.6) can be transformed to the shell coordinates (x, θ, z) by the following equation [31]:…”

Section: First Step: Natural Modesmentioning

confidence: 99%

“…The most diffused ones are probably the nonlinear normal modes (under this name are classified the techniques based on the centre manifold theorem, the normal form theory and the inertial manifold) [1][2][3][4][5][6][7][8][9], including the most diffused version with asymptotic approach, the discretization of the equations of motion by using global (i.e. defined on the whole structure) admissible functions [10][11][12][13], the proper orthogonal decomposition method [14][15][16][17][18] and the natural mode discretization [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell

Amabili

2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Reduced-order models are essential to study nonlinear vibrations of structures and structural components. The natural mode discretization is based on a twostep analysis. In the first step, the natural modes of the structure are obtained. Because this is a linear analysis, the structure can be discretized with a very large number of degrees of freedom. Then, in the second step, a small number of these natural modes are used to discretize the nonlinear vibration problem with a huge reduction in the number of degrees of freedom. This study finds a recipe to select the natural modes that must be retained to study nonlinear vibrations of an angle-ply laminated circular cylindrical shell that the author has previously studied by using admissible functions defined on the whole structure, so that an accuracy analysis is performed. The higher-order shear deformation theory developed by Amabili and Reddy is used to model the shell.

show abstract

Section: First Step: Natural Modesmentioning

confidence: 99%

Section: First Step: Natural Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell

Amabili

2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…As a consequence, in-plane inertia is retained in the equations of motions, which are derived via a Lagrangian approach [17][18][19]. In-plane inertia must be retained for shells that cannot be considered shallow.…”

Section: Introductionmentioning

confidence: 99%

“…In-plane inertia must be retained for shells that cannot be considered shallow. The effect of retaining or neglecting in-plane inertia has been addressed by Amabili [17] for closed circular cylindrical shells, and by Abe et al [20] for curved panels but only in the linear (natural frequencies) part of their study. As a consequence of taking into account these additional degrees-of-freedom, the computation of the LNMs is tedious and is thus bypassed by using as expansion functions an ad hoc basis verifying the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

Touzé

Amabili

Thomas

2008

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

. Reduced-order models for large-amplitude vibrations of shells including in-plane inertia. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197 (21-24) AbstractNon-linear normal modes (NNMs) are used in order to derive reduced-order models for large amplitude, geometrically non-linear vibrations of thin shells. The main objective of the paper is to compare the accuracy of different truncations, using linear and non-linear modes, in order to predict the response of shells structures subjected to harmonic excitation. For an exhaustive comparison, three different shell problems have been selected: (i) a doubly curved shallow shell, simply supported on a rectangular base; (ii) a circular cylindrical panel with simply supported, in-plane free edges; and (iii) a simply supported, closed circular cylindrical shell. In each case, the models are derived by using refined shell theories for expressing the strain-displacement relationship. As a consequence, in-plane inertia is retained in the formulation. Reduction to one or two NNMs shows perfect results for vibration amplitude lower or equal to the thickness of the shell in the three cases, and this limitation is extended to two times the thickness for two of the selected models.

show abstract

Conservative numerical methods for the Full von Kármán plate equations

Bilbao

Thomas

Touzé

et al. 2015

Numerical Methods Partial

View full text Add to dashboard Cite

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large-amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations.

show abstract

A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach

Cited by 172 publications

References 30 publications

Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell

Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell

Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

Conservative numerical methods for the Full von Kármán plate equations

Contact Info

Product

Resources

About