This investigation is concerned with axisymmetric as well as asymmetric vibrations of thin elastic spherical shells. First, with the limitation to torsionless axisymmetric motion, the basic equations for spherical shells of the classical bending theory of Love’s first approximation are reduced to a system of two coupled differential equations in normal displacement of the middle surface and a stress function; this system of equations is applied to free vibrations of a hemispherical shell with a free edge and numerical results are obtained for the lowest natural frequency as a function of the thickness of the shell. The remainder of the paper is, in the main, devoted to a study of asymmetric vibrations of a hemispherical shell with a free edge according to the extensional theory. Numerical results for natural frequencies (of the four lowest circumferential wave numbers) and mode shapes are given and the results are compared with the prediction of Rayleigh’s inextensional theory.
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On Vibrations of Elastic Spherical Shells
P. M. Naghdi
University of California, Berkeley, Calif.
Yale University, New Haven, Conn.
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Naghdi, P. M., and Kalnins, A. (March 1, 1962). "On Vibrations of Elastic Spherical Shells." ASME. J. Appl. Mech. March 1962; 29(1): 65–72. https://doi.org/10.1115/1.3636499
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