Geodesic
On some problems of reconstruction of inhomogeneous pre-stressed state in elastic solids
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 25-32

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Presents a general approach to the problem of reconstruction of the inhomogeneous pre-stressed state in an elastic body on its amplitude-frequency response, measured in part of its border. Based on the previously defined generalized reciprocity is the ratio of the sequence of linear ill-posed problems, allowing for refinement of the procedure for pre-stress tensor component. As an example, presented a series of computational experiments on the restoration of monotone functions of the distribution of pre-stressed state the problem of bending vibrations of a rod. 
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     title = {On some problems of reconstruction of inhomogeneous pre-stressed state in elastic solids},
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A. O. Vatulyan; V. V. Dudarev. On some problems of reconstruction of inhomogeneous pre-stressed state in elastic solids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 25-32. http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a3/