Method of generalized functions in boundary value problems of thermoelastic rod dynamics - L.A. Alexeyeva; M.M. Akhmetzhanova (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2020)
The method of generalized functions (GFM) has been developed to solve transient and vibrational boundary value problems of thermoelastic rod dynamics using a model of coupled thermoelasticity. Thermoelastic shock waves arising in such structures under the influence of shock loads and heat flows are considered. Conditions on their fronts were obtained. The singularity of the assigned boundary tasks taking into account shock waves has been proved. On the basis of GFM, a system of algebraic resolving equations is built for a wide class of boundary problems to determine their analytical solutions. Dynamics of the rod under the action of forces and heat sources of various types, including those described by singular generalized functions, which allow modeling the effect of pulsed concentrated sources, are studied. Computer implementation of solutions of one edge problem at stationary oscillations was carried out, results of numerical experiments of calculation of rod thermodynamics at low and high frequencies are presented. These solutions and algorithms can be used for engineering calculations of rod structures to evaluate their strength properties.