Title :
A mathematical model for small elastic disturbances propagation in strained solid continuum
Author :
Chekurin, V.F. ; Kravchyshyn, O.Z.
Author_Institution :
Pidstryhach Inst. for Appl. Problems of Mech. & Math., Acad. of Sci., Lvov, Ukraine
Abstract :
A mathematical model for the propagation of small elastic disturbances in a strained solid continuum is considered. The model is based on assumptions about the dependence of the acoustic parameters of the continuum on the initial strains. The model includes a system of hyperbolic partial differential equations, coefficients of which are dependent on the strain components. An iterative approach for solving this system of equations with specially dependent coefficients is developed. The approach enables taking into account, in the zero approximation, the influence of the integral parameters of the initial strain distribution on the elastic disturbance. Possibilities of utilizing the mathematical model to formulate the inverse problems of restorating the strain and stress fields are discussed
Keywords :
acoustic wave propagation; elasticity; hyperbolic equations; internal stresses; inverse problems; partial differential equations; stress-strain relations; acoustic parameters; hyperbolic partial differential equations; initial strain distribution; iterative approach; small elastic disturbance propagation; strain components; strain field restoration; strained solid continuum; stress field restoration; wave processes; Acoustic propagation; Capacitive sensors; Integral equations; Iterative methods; Mathematical model; Mathematics; Partial differential equations; Solids; Tensile stress; Thermal stresses;
Conference_Titel :
Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 2001. DIPED 2001. Proceedings of the 6th International Seminar/Workshop on
Conference_Location :
Lviv
Print_ISBN :
966-02-1876-1
DOI :
10.1109/DIPED.2001.965060
