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Free in-plane and out-of-plane vibrations of rotating thin ring based on the toroidal shell theory

Senjanović I., Ćatipović I., Alujević N., Čakmak D., Vladimir N.

Archives of Mechanics

2018

Vol. 70, nr 5

429--455

In this paper rigorous formulae for natural frequencies of in-plane and out-of-plane free vibrations of a rotating ring are derived. An in-plane vibration mode of the ring is characterised by coupled flexural and extensional deformations, whereas an out-of-plane mode is distinguished by coupled flexural and torsional deformations. The expressions for natural frequencies are derived from a generalised toroidal shell theory. For the in-plane vibrations, the ring is considered to be a short top segment of a toroidal shell. For the out-of-plane vibrations, the ring is considered to be a side segment of the shell. Natural vibrations are analysed by the energy approach. The expressions for the ring strain and kinetic energies are deduced from the corresponding expressions for the torus. It is shown that the ring rotation causes bifurcation of natural frequencies of the in-plane vibrations only. Bifurcation of natural frequencies of the out-of-plane vibrations does not occur. Otherwise, for non-rotating rings, the derived formulae for the natural frequencies of the in-plane and the out-of-plane flexural vibrations are very similar. The derived analytical results are validated by a comparison with FEM and FSM (Finite Strip Method) results, as well as with experimental results available in the literature.

Atmospheric Deposition Effects on Agricultural Soil Acidification State — Key Study : Krupanj Municipality

Čakmak D., Beloica J., Perović V., Kadović R., Mrvić V., Knežević J., Belanović S.

Archives of Environmental Protection

2014

Vol. 40, no. 2

137--148

Acidification, as a form of soil degradation is a process that leads to permanent reduction in the quality of soil as the most important natural resource. The process of soil acidification, which in the first place implies a reduction in soil pH, can be caused by natural processes, but also considerably accelerated by the anthropogenic influence of excessive S and N emissions, uncontrolled deforestation, and intensive agricultural processes. Critical loads, i.e. the upper limit of harmful depositions (primarily of S and N) which will not cause damages to the ecosystem, were determined in Europe under the auspices of the Executive Committee of the CLRTAP in 1980. These values represent the basic indicators of ecosystem stability to the process of acidification. This paper defines the status of acidification for the period up to 2100 in relation to the long term critical and target loading of soil with S and N on the territory of Krupanj municipality by applying the VSD model. The Inverse Distance Weighting (IDW) geostatistic module was used as the interpolation method. Land management, particularly in areas susceptible to acidification, needs to be focused on well-balanced agriculture and use of crops/seedlings to achieve the optimum land use and sustainable productivity for the projected 100-year period.