Vibration analysis of rotating toroidal shell by the Rayleigh-Ritz method and Fourier series

Senjanović, Ivo; Alujević, Neven; Ćatipović, Ivan; Čakmak, Damjan; Vladimir, Nikola

doi:10.1016/j.engstruct.2018.07.029

Cited by 37 publications

(31 citation statements)

References 30 publications

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“…For a closed, rotating toroidal shell the displacements components are assumed in the form, [9], Figure 1. where functions U(ϑ), V(ϑ) i W(ϑ) are the meridional, circumferential and radial displacement components of the cross-section, and ω is the natural frequency.…”

Section: Physical Meaning Of Strain and Kinetic Energy Terms Of Diffementioning

confidence: 99%

“…Substituting (1) into the corresponding expressions for strain and kinetic energies and performing integration over the circumferential angle within domain 0 -2π, the temporal variation vanishes and the strain and kinetic energies become time-invariant, [9]. This is due to the fact that the modes rotate while keeping a fixed circumferential profile.…”

Section: Fig 1 Geometry and Displacements Of Toroidal Shellmentioning

confidence: 99%

“…Recently, an analytical solution, the Rayleigh-Ritz method and the finite strip method have been developed for the use in vibration analysis of pressurized and rotating cylindrical and toroidal shells with closed and open cross-sections, [6][7][8][9][10]. An advantage of these methods is a considerable CPU time reduction in comparison to the classical FEM analysis [9]. Vibration analysis of a rotating ring has also been performed by reducing the governing equations of the toroidal shells, [11].…”

Section: Introductionmentioning

confidence: 99%

“…In the energy approach to tackling the problem of vibrations of pressurized and rotating toroidal shells some doubts were observed in [9], which are related to the physical meaning of energy terms of different order of displacements, the symmetry/antisymmetry of the Coriolis mass matrix and the influence of using the so-called engineering strains [12,13] in the analysis of the response of structures considered. A detailed and coherent explanation of the above doubts is given in the present paper.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells

Senjanović

Alujević

Ćatipović

et al. 2019

IJEM

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In this paper some dilemmas related to the application of the Rayleigh -Ritz method (RRM) in conjunction with the Fourier series for vibration and stability analysis of pressurized and rotating toroidal shells are elucidated. The physical meaning of the strain and kinetic energy terms of different order of displacements in the energy balance equation are explained. Only the second order terms remain in the variation of equation of motion. In the RRM, a symmetric Coriolis mass matrix is obtained as a result of using the energy approach. In FEM, the matrix equation of motion is complex and the Coriolis mass matrix is antisymmetric. It is shown that by transferring the equation of motion from the complex into the real domain, its size is doubled and the total Coriolis matrix becomes symmetric. The influence of using the Green-Lagrange non-linear strains and the engineering strains on vibration and buckling of a toroidal shell is contrasted. It is observed that differences in the dynamic analysis, due to the two different non-linear strain formulations, is quite small. On the contrary, in buckling analysis the engineering strains give considerably higher value of the critical load.

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Section: Physical Meaning Of Strain and Kinetic Energy Terms Of Diffementioning

confidence: 99%

Section: Fig 1 Geometry and Displacements Of Toroidal Shellmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells

Senjanović

Alujević

Ćatipović

et al. 2019

IJEM

View full text Add to dashboard Cite

show abstract

“…Li et al [7] analyzed the effects of hydrostatic pressure on the vibration of piezoelectric laminated cylindrical shell. Senjanović et al [8][9][10] studied the effects of internal pressure on vibrational behavior of rotating cylindrical shell. Arnold and Warburton [11,12] employed Hamilton's principle to derive equations of motion of the cylindrical shell.…”

Section: Introductionmentioning

confidence: 99%

Gas pressure and density effects on vibration of cylindrical pressure vessels: analytical, numerical and experimental analysis

2019

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The present research deals with the natural frequencies and mode shapes of cylindrical pressure vessels filled with different gasses in various internal pressures. The Hamilton's principle is employed to derive the governing equations, which are solved using analytical and finite element analyses, and a closed form relation as the equivalent density is obtained to include the gas properties. The experimental modal analysis is performed and the obtained results are compared and validated with analytical and finite element results. The results show that the type of the gas, as well as the gas pressure have significant effect on vibrational behavior of the structure and should be accounted in the design and analysis of vessels.

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$${\mathcal {H}}_{2}$$ H 2 optimization and numerical study of inerter-based vibration isolation system helical spring fatigue life

et al. 2018

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Vibration analysis of rotating toroidal shell by the Rayleigh-Ritz method and Fourier series

Cited by 37 publications

References 30 publications

Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells

Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells

Gas pressure and density effects on vibration of cylindrical pressure vessels: analytical, numerical and experimental analysis

$${\mathcal {H}}_{2}$$ H 2 optimization and numerical study of inerter-based vibration isolation system helical spring fatigue life

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