Abstract: Free across-the-thickness vibrations of a closed spherical shell consisting of three rigidly connected layers with arbitrary physical constants and thicknesses are studied. A closed-form solution in displacements to a one-dimensional (along the radius) vibration problem for a homogeneous spherical shell is derived and then used in posing a boundary-value problem on free vibrations of a heterogeneous sphere. Based on the degeneration of the sixth-order determinant of a system of homogeneous equations satisfying the corresponding boundary conditions, a transcendental equation for eigenfrequencies is found. Transformation variants for the equation of eigenfrequencies in the cases of degeneration of physical and geometric parameters of the compound shell are considered. The main attention in investigating the lowest frequency is given to its dependence on the structure of shell wall, whose parameters greatly affect the calculated values of the high-frequency vibration spectrum of the shell.
B I B L I O G R A F I A1. V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayer Structures [in Russian], Mashinostroenie, Moscow (1980).
2. M. E. Raville, E. S. Ueng, and M. M. Lei, “Natural frequencies of vibration of fixed-fixed sand wich beams,” ASME J. Appl. Mech., 28, 367–371 (1961).
3. S. Kadyrov and V. Skvortsov, “Dynamic transient response of shallow sandwich panel subjected to pressure field,” in: O. T. Thomsen, E. Bozhevolnaya and A. Lyckegaard (eds.), Sandwich Structures. 7: Advancing with Sandwich Structures and Materials, Proc. 7th Int. Conf. on Sandwich Structures, 29–31 August, 2005, Denmark, Aalborg, Springer, Netherlands (2005), pp. 519–526.
4. J. Hohe and L. Librescu, “A nonlinear theory for doubly curved anisotropic sand wich shells with trans versely compressible core,” J. Solids Struct., 40, 1059–1088 (2003).
5. S. V. Sorokin, “Analysis of wave propagation in sandwich plates with and without heavy fluid loading,” J. Sound Vibr., 36, 1039–1062 (2004).
6. I. N. Sneddon and D. S. Berry, Classical Theory of Elasticity, Handbuch der Physik. Vol. 6, Springer (1958).
7. V. A. Polyakov, R. P. Shlitsa, V. V. Khitrov, and V. I. Zhigun, “An applied model for free radial vibrations of a closed spherical sandwich shell,” Mech. Compos. Mater., 43, No. 4, 331–344 (2007).
8. N. S. Koshlyakov, E. B. Gliner, and M. M. Smirnov, Partial Differential Equations of Mathematical Physics [in Russian], Vysshaya Shkola, Moscow (1970). 
Pełny tekst 
DOI 
Web of Science 
YADDA/CEON