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The problem of thermoelastic oscillations of connected to a spacecraft rod with solar heating and considering of heat radiation

Grishanina T.V., Russkikh S.V., Shklyarchuk F.N.

#### Abstract:

Thermoelastic flexural vibrations of a thin-walled rod with a circular cross section connected by an elastic-viscous hinge to a spacecraft and subjected to direct solar radiation are considered taking into account the heat flux lost due to external radiation into outer space and radiant heat transfer on the inner surface of the rod shell. The change of the angles of the sun rays incidence on the surface of the rod due to its bending and turning together with the spacecraft is taken into account. The equation for the nonstationary thermal conductivity of a thin cylindrical shell of a rod is solved by expanding the heat fluxes and temperature in a series of cosines in the circumferential direction, with only axially symmetric and antisymmetric harmonics held, neglecting the temperature change in the axial direction. It is reduced to two first-order nonlinear differential equations connected with each other and with the displacement of the rod for the axisymmetric and antisymmetric components of the temperature in the considered cross-section of the rod. To solve the nonstationary problem of thermoelasticity and thermal conductivity of the rod, the finite element method is used. In this case, the bend is approximated along the length of the finite element by an exact solution of the static problem, and the temperature by a linear function. The potential energy of thermoelastic bend of the final element of the rod is recorded through its transverse displacements, angles of rotation and antisymmetric components of temperature at the ends. When calculating the kinetic energy of rotation of the system and the relative flexural vibrations of the rod with a solid body at the end, the rod is modeled by the concentrated masses and moments of inertia reduced to the cross-sections separating the finite elements. A system of nonlinear ordinary differential equations for unknown functions – the angle of rotation of the spacecraft, transverse displacements, rotation angles, axisymmetric and antisymmetric temperature components in the calculated cross-sections of the finite element model of the rod is obtained. The dynamic behavior of the system is calculated when it leaves the shadow with estimates of the convergence and stability of the numerical solution. The influence of heat radiation and some elastic parameters of the rod on the oscillations of the system is studied.

#### Keywords:

elastic-viscous hinges,

FINITE-ELEMENT METHOD,

heat radiation,

SOLAR HEATING,

SPACE VEHICLES,

THERMOELASTIC VIBRATIONS,

thin-walled rods,

космические аппараты,

метод конечных элементов,

солнечный нагрев,

теплоизлучение,

термоупругие колебания,

тонкостенные стержни,

упруго-вязкие шарниры
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