BOUNDARY VALUE PROBLEMS OF THERMOELASTIC RODS DYNAMICS AND THEIR
GENERALIZED SOLUTIONS
Abstract
Rod structures are widely used in mechanical engineering as connecting
and transmission links for structural elements of a wide variety of
machines and mechanisms. During operation, they are subject-ed to
variable mechanical and thermal influences, which create a complex
stress-strain state in structur-al elements, depending on their
temperature, and affecting their strength and reliability. Therefore,
the determination of the thermally stressed state of rod structures,
taking into account their mechanical properties (in particular,
elasticity and thermal conductivity) is one of the topical scientific
and tech-nical problems. Here, spatially one-dimensional unsteady
boundary value problems (BVPs) of uncoupled ther-moelasticity are
considered, which can be used to study various bar structures. This
model describes well thermodynamic processes at low strain rates and
here a unified technique is proposed for solving various BVPs typical of
practical applications. Problems of determining the thermally stressed
state of a thermoelastic rod using a model of uncoupled thermoelasticity
are considered. Generalized solutions of non-stationary and stationary
direct and semi-inverse BVPs under the action of power and heat sources
of various types are con-structed on the basis of the method of
generalized functions. Acting sources can also be specified by singular
generalized functions, under different boundary conditions at the ends
of the rod. Con-sidered are shock elastic waves that arise in such
structures under the action of shock loads. Regu-lar integral
representations of generalized solutions are obtained, which give an
analytical solution to the stated BVPs.