Relations from a linear, kinematically nonuniform model of a layered shell were used to construct a system of motion equations for an M-layered shallow shell which considered all components of the stress-strain state and inertia of the shell. It was shown using sample calculations of the natural frequency spectrum of physically uniform and hybrid threelayer hells that this model makes it possible in a linear approximation to calculate the complete natural-frequency spectrum of layered shells. It can be used in engineering calculations of the dynamic characteristics of shells in which relatively thin and stiff bearing layers alternate in the packet with layers of a “soft“ filler (structurally nonuniform hybrid shells).
The use of simplified (classical) models, refined kinematically uniform models, and nonuniform models not accounting for compressive strains in the shell layers, etc. (see [1, 5]) is limited to the classes of physically uniform and quasiuniform shells and to cases of calculation of the dynamic characteristics determined by three fundamental frequencies of the shell when regarded as a three-dimensional body.
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P. P. Chulkov, “Equations of vibrations of elastic layered shells”, in: Continuum Dynamics [in Russian], Vol. 4, Novosibirsk (1970), pp. 19–29.
V. L. Narusberg, “Formulation of problems of optimizing macroscopically uniform layered shells designed for stability”, Mekh. Kompozitn. Mater., No. 4, 648–656 (1983).
E. I. Grigolyuk and F. A. Kogan, “Current state of the theory of multilaminate shells”, Prikl. Mekh.,8, No. 6, 3–17 (1972).
A. S. Vol'mir, Nonlinear Dynamics of Plates and Shells [in Russian], Moscow (1972).
G. A. Teters, R. B. Rikards, and V. L. Narusberg, Optimization of Shells Made of Laminated Composites [in Russian], Riga (1978).
V. L. Narusberg and L. A. Pazhe, “Efficient structure for the reinforcement of a thickwalled three-layered cylindrical shell designed for vibration resistance or for static stability under external pressure”, Mekh. Kompozitn. Mater., No. 2, 283–288 (1984).
V. L. Narusberg, “Establishment of a uniform model of a layered composite in problems of optimization of thin-walled shells designed for stability”, ibid., No. 3, 474–479 (1981).
V. N. Kobelev, L. M. Kovarskii, and S. I. Timofeev, Design of Three-Layer Structures (Handbook) [in Russian], Moscow (1984).
Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 298–304, March–April, 1985.
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Narusberg, V.L., Pazhe, L.A. Calculation of the natural-vibration spectra of layered shells of moderate thickness. Mech Compos Mater 21, 206–211 (1985). https://doi.org/10.1007/BF00617694
- Dynamic Characteristic
- Linear Approximation
- Frequency Spectrum
- Fundamental Frequency
- Engineering Calculation