Abstract
From preset pressure values on both surfaces of a plate, its bending is determined depending not only on the pressure difference but also on the product of the average pressure and the curvature of the middle surface. The latter component of this action is determined according to the models of Kirchhoff and Timoshenko for the case of a cylindrical linear bending of a plate. It is shown that taking into account the average pressure leads to an increase in the effective flexural rigidity. The value of deflection according to the models of Kirchhoff and Timoshenko is compared with a classical result. A criterion is established for the situation where the influence of the ambient pressure on the plate bending can be significant. The effect of the average pressure exerted on the longitudinal stability of the plates is determined.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Timoshenko, S., Young, D.H., and Weaver, W., Jr., Vibration Problems in Engineering, New York: Wiley, 1974.
Vol’mir, A.S., Nelineinaya dinamika plastin i obolochek (Nonlinear Dynamics for Plates and Shells), Moscow: Nauka, 1972.
Il’gamov, M.A., Static Problems of Hydroelasticity, Moscow: Nauka, Fizmatlit, 1998.
Il’gamov, M.A., The interaction of instabilities in a hydroelastic system, Appl. Math. Mech., 2017, vol. 80, pp. 400–408.
Pisarenko, G.S., Yakovlev, A.P., and Matveev, V.V., Spravochnik po soprotivleniyu materialov (Materials Strength. Handbook), Kiev: Naukova Dumka, 1988.
Ishlinskii, A.Yu., Research of elastic systems stability in terms of mathematical elastic theory, Ukr. Mat. Zh., 1954, vol. 6, no. 2, pp. 140–146.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.A. Il’gamov, 2017, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2017, No. 5, pp. 30–35.
About this article
Cite this article
Il’gamov, M.A. On the effect of ambient pressure on the bending of a plate. J. Mach. Manuf. Reliab. 46, 442–447 (2017). https://doi.org/10.3103/S1052618817050089
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1052618817050089