Method of generalized functions in boundary value problems of thermoelastic rod dynamics

Abstract

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.