Stressed State of a Hollow Conducting Sphere under the Electromagnetic Action in the Decaying Sinusoid Mode
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STRESSED STATE OF A HOLLOW CONDUCTING SPHERE UNDER THE ELECTROMAGNETIC ACTION IN THE DECAYING SINUSOID MODE R. S. Musii
UDC 539.3
We formulate a dynamic centrally symmetric problem of thermomechanics for a hollow conducting sphere subjected to a homogeneous nonstationary electromagnetic action in the decaying sinusoid mode. We obtain the solution of this problem by using the cubic approximations of the azimuthal component of the vector of magnetic field and the radial component of the stress tensor in the radial coordinate. We also perform the numerical analysis of the thermal stressed state and the load-carrying capacity of nonferromagnetic spheres under the indicated conditions. Keywords: dynamic centrally symmetric problem of thermomechanics, conducting sphere, electromagnetic action, decaying sinusoid mode, resonance frequency, load-carrying capacity.
Investigations of the elastic equilibrium of structural elements under the complex action of force, temperature, and electromagnetic loads form a basis for the prediction of their strength and reliability and decreasing their mass and materials consumption, which is quite important for different branches of industry, instrument making, and power engineering. In numerous technical devices subjected to the action of various physical fields and, in particular, pulsed electromagnetic fields (EMF) with amplitude modulation, the role of a structural element is often played by a hollow metallic sphere. The contemporary technologies of pulse treatment [1–6] often use pulsed EMF with amplitude modulation and, in particular, in the decaying sinusoid mode (DSM) [3, 5–8]. These EMF form nonstationary temperature fields and stresses in spherical conducting elements, which may reach high values for the corresponding parameters of pulsed EMF, up to the loss of the load-carrying capacity of structural elements. In [4, 9–12], one can find a description of the dynamic behavior of a hollow sphere under pulsed force and thermal actions. The thermal stressed state of a sphere under the influence of electromagnetic pulses is studied in [13, 14]. A similar problem for the electromagnetic action with pulsed modulating signals is analyzed in [15]. However, the stressed state of a sphere of this kind under the electromagnetic action in the DSM is not investigated. In the present work, we obtain the solution of a dynamic centrally symmetric problem of thermomechanics for a hollow conducting sphere and investigate its thermomechanical behavior and load-carrying capacity under the electromagnetic action in the DSM for frequencies of the carrier signal lying outside the range of resonance frequencies and equal to the first resonance frequency. Statement of the Problem Consider a conducting hollow sphere referred to a spherical coordinate system (r, ϕ, θ) whose center coin-
cides with the center of the sphere. The sphere is subjected to the action of a pulsed EMF in the DSM specified by “L’vivs’ka Politekhnika” National University, Lviv, Ukraine; e-mail: [email protected]. Translated from
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