Abstract
The paper proposes a numerical-analytic approach to studying the free vibrations of orthotropic shallow shells with double curvature and rectangular planform. The approach is based on the spline-approximation of unknown functions. Calculations are carried out for different types of boundary conditions. The influence of the mid-surface curvature and variable thickness on the behavior of dynamic characteristics is studied
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. A. Ambartsumyan, General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).
A. Ya. Grigorenko, “Calculation of natural vibrations of rectangular plates with varying thickness by the spline-collocation method,” Prikl. Mekh., 26, No. 12, 116–119 (1990).
Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar’, Free Vibrations of Members of Shell Structures [in Russian], Naukova Dumka, Kyiv (1986).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells of Variable Stiffness, Vol. 4 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1981).
L. V. Kurpa and A. V. Chistilina, “Investigation of free vibrations of multilayer shallow shells and plates of complex shape in plan,” Strength of Materials, 35, No. 2, 183–191 (2003).
S. G. Lekhnitskii, Anisotropic Elasticity Theory [in Russian], Nauka, Moscow (1977).
I. A. Birger and Ya. G. Panovko (eds.), Strength, Stability, Vibrations: A Handbook [in Russian], Vol. 3, Mashinostroenie, Moscow (1968).
P. M. Varvak and A. F. Ryabov (eds.), A Handbook on the Theory of Elasticity [in Russian], Budivel’nyk, Kyiv (1971).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichehko, “Stress-strain analysis of orthotropic closed and open noncircular cylindrical shells,” Int. Appl. Mech., 41, No. 7, 778–785 (2005).
A. Ya. Grigorenko and T. L. Efimova, “Spline-approximation method applied to solve natural-vibration problems for rectangular plates of varying thickness,” Int. Appl. Mech., 41, No. 10, 1161–1169 (2005).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichehko, “Stress analysis of noncircular cylindrical shells with cross-section in the form of connected convex half-corrugations,” Int. Appl. Mech., 42, No. 4, 431–438 (2006).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichehko, “Stress-strain solutions for circumferentially corrugated elliptic cylindrical shells,” Int. Appl. Mech., 42, No. 9, 1021–1028 (2006).
J. K. Lee, A. V. Leissa, and A. J. Wang, “Vibrations of blades with variable thickness and curvature by shell theory,” Trans. ASME, J. Eng. Gas Turb. Power, 106, 11–16 (1984).
K. M. Liew, C. W. Lim, and S. Kitipornchai, “Vibration of shallow shells: A review with bibliography,” Appl. Mech. Rev., 50, No. 8, 431–444 (1997).
K. M. Liew and C. W. Lim, “Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness,” Inst. Aerounaut. Astronaut. J., 32(2), 387–396 (1998).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 102–115, June 2007.
Rights and permissions
About this article
Cite this article
Budak, V.D., Grigorenko, A.Y. & Puzyrev, S.V. Free vibrations of rectangular orthotropic shallow shells with varying thickness. Int Appl Mech 43, 670–682 (2007). https://doi.org/10.1007/s10778-007-0066-y
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-007-0066-y