The Rayleigh and Courant variational principles in the six-parameter shell theory

Eremeyev, Victor A.; Lébedev, Leonid P.; Cloud, Michael J.

doi:10.1177/1081286514553369

Cited by 31 publications

(15 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Amplitude and vibration frequency at lock-in are estimated according to equations (21) and (22). Numerical results are obtained taking into account (2DOF) and neglecting (1DOF) the coupling between torsion and lateral vibrations.…”

Section: Numerical Examplesmentioning

confidence: 99%

On the effect of mechanical non-linearities on vortex-induced lock-in vibrations

Piccardo

Tubino

Luongo

2016

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Vortex-induced vibrations at lock-in conditions are modeled through generalized van der Pol-Duffing oscillators endowed with frequency-dependent coefficients, taking inspiration from fluid-elastic models. Accordingly, it is found that the limit-cycle amplitude and the non-linear frequency are mutually dependent (feedback effect), differently from the classic oscillator behavior. Consequently, the mechanical non-linearities, which are often believed to be unimportant, do affect the amplitude of motion. Examples concerning an ideal one degree-of-freedom van der Pol-Duffing oscillator and a two degree-of-freedom model, coarsely representative of a tower building, confirm the importance of this approach also from a technical point of view. Thus, non-linear geometric terms and modal interaction (even in non-resonant cases) can lead to non-negligible modifications of purely aeroelastic problems

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

On the effect of mechanical non-linearities on vortex-induced lock-in vibrations

Piccardo

Tubino

Luongo

2016

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…Homogenization modelling of a laminate material [19] is based on the theory of mixtures cells. The first variation of free torsional vibration frequencies with respect to variations of the design variation is derived by means of variational calculus [6,7,13]. A numerical example of the paper deals with a simply supported I-beam.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

Szymczak

Kujawa

2019

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

The paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too. Keywords Sensitivity analysis • Free torsional vibration frequencies • Thin-walled beams • Analytical solution • FEM Communicated by Andreas Öchsner.

show abstract

“…Theoretical basis can be traced back to works of Reissner [4] and Libai and Simmonds [5]. Further theoretical developments and aspects of numerical formulation can be found for instance in [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…The resulting kinematic model is formally equivalent to the Cosserat surface with three rigidly rotating directors.Theoretical basis can be traced back to works of Reissner [4] and Libai and Simmonds [5]. Further theoretical developments and aspects of numerical formulation can be found for instance in [6][7][8][9][10][11].In the previous works e.g. [12][13][14][15][16][17] the constitutive relation had in some sense postulated character.…”

mentioning

confidence: 99%

Geometrically nonlinear FEM analysis of 6‐parameter resultant shell theory based on 2‐D Cosserat constitutive model

2015

View full text Add to dashboard Cite

We develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6‐parameter shell theory. The Cosserat plane stress equations are integrated through‐the‐ thickness under assumption of the Reissner‐Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar characteristic length l. Based on FEM simulations we evaluate their influence on the behaviour of shell models in the geometrically nonlinear range of deformations.

show abstract

The Rayleigh and Courant variational principles in the six-parameter shell theory

Cited by 31 publications

References 63 publications

On the effect of mechanical non-linearities on vortex-induced lock-in vibrations

On the effect of mechanical non-linearities on vortex-induced lock-in vibrations

Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

Geometrically nonlinear FEM analysis of 6‐parameter resultant shell theory based on 2‐D Cosserat constitutive model

Contact Info

Product

Resources

About