Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

Moussaoui, Fadila; Benamar, Rhali

doi:10.1006/jsvi.2001.4146

Cited by 75 publications

(20 citation statements)

References 124 publications

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“…A modal expansion solution exists for the case of a cantilevered von Karman plate [45], but analytical, closed form solutions are not available for most other cases with general boundary conditions. A number of approximate methods exist, however, that can accurately model von Karman plates and shells [46]. Approximate methods include finite elements, both spline finite strip methods [47] and hierarchical finite element methods [43,44], incremental harmonic balance [48], nonlinear normal modes [49], and assumed displacement fields with Taylor series expansions in the normal directions [50].…”

Section: Introductionmentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled "Reduced Order Modeling of Fluid/Structure Interaction." This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convectiondiffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.

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Section: Introductionmentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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“…The main objectives of the study of shell structures under dynamic loading are to investigate their stability, strength and vibrations as evidenced by review articles and monographs [13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Models of Deformation of Stiffened Orthotropic Shells under Dynamic Loading

Semenov¹,

Семенов²

2016

J. Sib. Fed. Univ., Math. phys.

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“…Readers interested by these works can turn to [1] and [2] or to the review paper presented recently by [3], and to a more recent review paper by [4], in which a set of papers are discussed and commented. It can be observed that although several works exist in literature on nonlinear vibrations of shells, only few papers are available which are concerned with the nonlinear free vibration of shells of infinite length.…”

Section: Introductionmentioning

confidence: 99%

Effects of in-plane inertia on natural frequency and stresses of long circular cylindrical shell

Rougui

Karimin

2012

MATEC Web of Conferences

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Abstract. In this paper an analytical procedure is given to study the free-vibration characteristics of thin long circular cylindrical shells with simply supported boundary conditions. An approach based on Sander's nonlinear theory and Lagrange equations is employed. Influence of in-plane inertia on natural frequencies and stress for several modes shape is discussed. Natural frequencies for a number of particular cases are evaluated and compared with some available experimental and other analytical results in the literature. The distributions of the bending and axial stresses associated with the nonlinear modes shape are given and compared with those obtained via the linear theory.

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Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

Cited by 75 publications

References 124 publications

Reduced order modeling of fluid/structure interaction.

Reduced order modeling of fluid/structure interaction.

Models of Deformation of Stiffened Orthotropic Shells under Dynamic Loading

Effects of in-plane inertia on natural frequency and stresses of long circular cylindrical shell

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