A plane axisymmetrical coupled dynamic problem of thermomechanics for an electroconductive hollow cylinder under homogeneous non-stationary electromagnetic action is formulated. To construct its solution, the approximation of the determining functions the axial component of the magnetic field strength vector, the temperature, and the radial component of the displacement vector with respect to the radial variable by cubic polynomials is used. As the result, the initial-boundary problem for determining functions is reduced to a Cauchy problem with respect to the time variable for the integral characteristics of these functions. The expressions of integral characteristics are obtained in the form of a convolution of functions describing the uniform solutions and the given limit values of determining functions. As an example, the amplitude-frequency characteristics of the radial stresses in the given cylinder are analyzed numerically, with taking into account the connectivity between the temperature and the displacement fields as well as without such accounting.
Using the approximation of the distributions of the axial component of the magnetic field stress vector, of temperature and radial displacements in the radial variable by cubic polynomials, we obtain a general solution of the connected dynamic problem of thermomechanics for an electric conductive hollow cylinder under the action of impulsed electromagnetic fields with amplitude modulation of characteristic types in modes with the impulsed modular signal, the damped sinusoid and the single electromagnetic impulse equal to the modular signal.
A rectangular isotropic two-layer plate of an irregular structure is considered, the edges of which are freely supported, and a constant temperature is maintained on them. Two-dimensional Kirchhoff-type thermoelasticity equations and two-dimensional heat equations written for an inhomogeneous material were used to study the temperature stresses in the plate. Using the method of double trigonometric series in spatial variables and the Laplace integral transformation over time, the general solutions of boundary value problems of thermoelasticity and heat conductivity for this plate under the action of a locally distributed temperature field specified at the initial moment of time are written down. The normal stresses in the layers of the plate are numerically analyzed depending on the geometric parameters, heat transfer coefficient, and time.
A physical and mathematical model for determining the thermostressed state of an electrically conductive cylindrical implant under the action of external unstable electromagnetic fields, in particular the impulse with amplitude modulation, is proposed. This model allows predicting the maximum allowable values (according to physiological norms) of temperature and stress intensities in the considered implant depending on the parameters of external unstable electromagnetic fields and the time of their action.
A physical and mathematical model for determining the thermostressed state of an electroconductive solid ball under the action of an amplitude modulated radioimpulse is proposed. The centrally symmetric problem of thermomechanics for the considered ball is formulated. The azimuthal component of the magnetic field strength vector, temperature, and the radial component of the displacement vector were chosen as the determining functions. To construct solutions of the formulated components of the initial-boundary value problems of electrodynamics, heat conductivity, and thermoelasticity, a polynomial approximation of the determining functions over the radial variable is used. As a result, the initial-boundary value problems on the determining functions are reduced to the corresponding Cauchy problems on the integral characteristics of these functions over the radial variable. General solutions of Cauchy problems under homogeneous nonstationary electromagnetic action are obtained. Based on these solutions, the change in time of Joule heat, ponderomotor force, temperature and stresses in the ball under the action of amplitude-modulated radioimpulse depending on its amplitude-frequency characteristics and duration is numerically analyzed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.