Vibrations of Compound Shell Systems Under Subcritical Loads
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International Applied Mechanics, Vol. 56, No. 4, July, 2020
VIBRATIONS OF COMPOUND SHELL SYSTEMS UNDER SUBCRITICAL LOADS
E. I. Bespalova and N. P. Boreiko
The effect of various static subcritical axisymmetric loads on the natural frequencies of elastic systems composed of shells of revolution with different geometry is analyzed. Some features of the low-frequency spectrum of vibrations of compound systems are illustrated and compared with the frequencies of some zero-curvature shells. Keywords: compound shell of revolution, axisymmetric loads, subcritical state, vibrations Introduction. The paper continues the studies [1, 4] on the vibrations of compound systems of thin (flexible) shells of revolution of different shapes and structures under axisymmetric static loads. Such loads (thermal fields, mechanical loads, radiation, aggressive media, etc.) in many cases are natural operation conditions for underwater vehicles, spacecraft, various vessels, etc. Depending on their behavior and intensity, static fields can strongly influence the spectrum of natural frequencies of shell objects. Therefore, it is important to take into account these loads in analyzing the dynamical characteristics of elastic structures. Moreover, the results obtained in studying the vibrations of deformable systems with allowance for the stress–strain state induced by static fields underlie the dynamical stability criterion where the minimum natural frequency becomes zero under the critical loads. The published studies in this field of the mechanics of deformable systems have allowed for static loads only for elements of simple shapes such as plates, cylinders, cones, spherical segments, etc. For example, the preloads in the form of shear forces and biaxial stress state were taken into account in [3, 10, 14] in analyzing the vibrations of orthotropic plates made of nano- and piezomaterials, resting on a Pasternak viscoelastic foundation, and subjected to various boundary conditions. The static axisymmetric fields induced by external or internal hydrodynamic pressure and centrifugal and Coriolis forces are considered in studying the dynamic characteristics of cylindrical shells made of orthotropic and functionally graded materials depending on the geometrical parameters, the interaction with fluid, the speed of rotation, etc. [18, 19, 21]. Almost the same loads are considered in analyzing the frequency characteristics of conical shells. For example, shells with considerable piecewise inhomogeneity across the thickness were addressed in [11, 12, 17], where the expressions for centrifugal and Coriolis forces were refined and the influence of rotation speed on the natural frequencies of a truncated cone with different conicity angles and physical and mechanical properties of the composite material were analyzed. In [15], the vibrations of large roofs in the form of open cylindrical shells and shells with two-fold curvature undergoing seismic loads were considered taking into account the vertical and horizontal components of the loads and stressin
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