PSI - Issue 72

Alexander Kamenskikh et al. / Procedia Structural Integrity 72 (2025) 252–259

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Δ T =10 °С

Δ T =40 °С

Fig. 5. Normal displacement fields of a plate rigidly clamped at all edges under the action of temperature load Δ T

The analysis of the above results allows us to conclude that, as the temperature load increases, the lowest frequency of the hollow shell vibration decreases until the buckling. After that, the mode corresponding to it leaves the spectrum, and further increase in the temperature load leads to an increase in the low frequency until there is another change in the order of natural modes in the spectrum. It should be noted that the natural frequencies of the shell with small curvature ( H/h =0, H/h =5) rigidly clamped at all edges are significantly affected by the temperature load, since the bu ckling occurs at a small value of Δ T cr . As the ratio H / h increases, the effect of temperature load on the natural frequencies decreases.

Fig. 6. Normal displacements ( a ) and lowest natural frequencies of vibration ( b ) of shells for different values of the parameter H/h (FCFС)

Similar calculations were performed for shells with FCFC boundary condition (Fig. 6). The behaviour of natural frequencies of vibration for structures with FCFC and CCCC variants of clamping is qualitatively similar (see Fig. 2 a and Fig.6 a ). The difference is in the rate of variation of the frequency  1 with temperature load. The rate is higher for the shell rigidly clamped at all edges. Such boundary conditions lead to a sharper increase in thermal stresses, which increases the sensitivity of natural frequencies to temperature changes. Acknowledgements The study was made in the framework of the government task, registration number of the theme 124020700047 3. References Meyers, C.A., Hyer, M.W., 1991. Thermal buckling and postbuckling of symmetrically laminated composite plates. Journal of Thermal Stresses 14(4), 519 – 540 Prabhu, M.R., Dhanaraj, R., 1994. Thermal buckling of laminated composite plates. Computers & Structures, 53, No. 5, 1193 – 1204 Azzara, R., Carrera, E., Pagani, A., 2022. Nonlinear and linearized vibration analysis of plates and shells subjected to compressive loading. International Journal of Non-Linear Mechanics 141, 103936