Transient dynamics of a thin isotropic spherical belt

DOI: 10.34759/trd-2023-131-05

Аuthors

Zuskova V. N.^*, Okonechnikov A. S.^**, Serdyuk D. O.^***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: varvarazuskova@gmail.com
**e-mail: leon_lionheart@mail.ru
***e-mail: d.serduk55@gmail.com

Abstract

Thin-walled spherical shells are common structural elements in various industries, such as aircraft, rocket and mechanical engineering. When designing the corresponding structural elements, one of the topical issues is the calculations of structures operating in non-stationary interaction modes. Such calculations are complex and time-consuming, since in such problems the desired solution is significantly heterogeneous in spatial coordinates and time. In an axisymmetric formulation, the study of the transient dynamics of a thin spherical belt with emission boundary conditions under the influence of a moving transient load. The belt material is elastic and isotropic. The Kirchhoff-Love hypothesis was implemented in the qualitative mathematical model of the spherical scenario. An approach to research based on the principle of superposition, the Green’s function method and the method of compensating influence. The essence of the results is in connection with the desired solution with the acting and compensating load using integral operations such as convolution in coordinate and time. Being this operation, is the Green’s function for spherical exploitation, which is the normal displacement in response to the core, random focusing on the load coordinate and time, mathematically described by the Dirac delta function. The compensation solution is the result of studying some specially calculated values, at which decisions are made from the acting load and the compensating sensation, satisfying the boundary conditions at the ends of the spherical belt. An example of calculating the unsteady dynamics of a spherical belt is given. The results for transient functions of normal displacements, angles of turns and bending moments are presented in the form of graphs. The method of compensating loads applied in the work allows us to study the transient dynamics of a spherical belt with intermediate axisymmetric supports, as well as spherical segments.

Keywords:

transitional dynamics, compensating load, Green's function, spherical layer, spherical shell

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