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Analytic solution of one-dimensional problem for partial integro-differential equations which have partial continuous coefficients in thermoviscoelasticity theory

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 1998-1999
Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
in this paper, a non-stationary problem on thermomechanic wave propagation is solved in an environment, which is, consists of a finite thick plate connected with a semiinfinile space. Materials of the plate and the space are in conformity with linear viscoelaslicity laws. Mathematical model of (he problem consists of: linear equations of viscoelasticity and heat transfer for each environment independently, initial conditions and on the connection surface of environments conditions of increasing temperature and normal stress, depending only on time which are given as known functions, it is assumed that temperature and mechanical fields depend on each other. As a system, parabolic type partial inlegro-differential equation of temperature and hyperbolic type partial integro-differential equation of wave are solved, it is assumed that kernels of integral operators are difference kernels. Depending on boundary conditions, functions of temperature and mechanical magnitudes become only functions of time and a space axis, which is perpendicular to free surface. In this case the problem turns out to be a one-dimensional one.
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