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

Senjanović, Ivo; Alujević, Neven; Ćatipović, Ivan; Čakmak, Damjan; Vladimir, Nikola; Lozina, Željan
Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells // International journal for engineering modelling, 32 (2019), 1; 59-76 doi:10.31534/engmod.2019.1.ri.01f (međunarodna recenzija, članak, znanstveni)

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

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

Izvornik
International journal for engineering modelling (1330-1365) 32 (2019), 1; 59-76

Ključne riječi
toroidal shell ; vibration ; buckling ; energy formulation ; geometric stiffness matrix ; Coriolis mass matrix

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Strojarstvo, Zrakoplovstvo, raketna i svemirska tehnika, Temeljne tehničke znanosti

Ustanove:
Fakultet elektrotehnike, strojarstva i brodogradnje, Split,

#### Citiraj ovu publikaciju:

Senjanović, Ivo; Alujević, Neven; Ćatipović, Ivan; Čakmak, Damjan; Vladimir, Nikola; Lozina, Željan
Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells // International journal for engineering modelling, 32 (2019), 1; 59-76 doi:10.31534/engmod.2019.1.ri.01f (međunarodna recenzija, članak, znanstveni)
Senjanović, I., Alujević, N., Ćatipović, I., Čakmak, D., Vladimir, N. & Lozina, Ž. (2019) Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells. International journal for engineering modelling, 32 (1), 59-76 doi:10.31534/engmod.2019.1.ri.01f.
@article{article, author = {Senjanovi\'{c}, Ivo and Alujevi\'{c}, Neven and \'{C}atipovi\'{c}, Ivan and \v{C}akmak, Damjan and Vladimir, Nikola and Lozina, \v{Z}eljan}, year = {2019}, pages = {59-76}, DOI = {10.31534/engmod.2019.1.ri.01f}, keywords = {toroidal shell, vibration, buckling, energy formulation, geometric stiffness matrix, Coriolis mass matrix}, journal = {International journal for engineering modelling}, doi = {10.31534/engmod.2019.1.ri.01f}, volume = {32}, number = {1}, issn = {1330-1365}, title = {Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells}, keyword = {toroidal shell, vibration, buckling, energy formulation, geometric stiffness matrix, Coriolis mass matrix} }
@article{article, author = {Senjanovi\'{c}, Ivo and Alujevi\'{c}, Neven and \'{C}atipovi\'{c}, Ivan and \v{C}akmak, Damjan and Vladimir, Nikola and Lozina, \v{Z}eljan}, year = {2019}, pages = {59-76}, DOI = {10.31534/engmod.2019.1.ri.01f}, keywords = {toroidal shell, vibration, buckling, energy formulation, geometric stiffness matrix, Coriolis mass matrix}, journal = {International journal for engineering modelling}, doi = {10.31534/engmod.2019.1.ri.01f}, volume = {32}, number = {1}, issn = {1330-1365}, title = {Some dilemmas in energy approach to vibration and stability analysis of pressurized and rotating toroidal shells}, keyword = {toroidal shell, vibration, buckling, energy formulation, geometric stiffness matrix, Coriolis mass matrix} }

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