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On the domain of variation of added masses, polarization and effective characteristics of composites. (English. Russian original) Zbl 0786.76018

J. Appl. Math. Mech. 56, No. 1, 102-107 (1992); translation from Prikl. Mat. Mekh. 56, No. 1, 118-123 (1992).
Summary: The well-known result of Pólya of Schiffer [M. Schiffer, C. R. Acad. Sci., Paris 244, 26, 3118-3121 (1957; Zbl 0080.083)] concerned with an estimate for the added mass (AM) and polarization tensors is improved. The exact domain of variation of the AM and polarization tensors for a body of fixed volume is found. It is shown that the estimates of the possible values of the effective conductivity matrix known in the theory of composite materials are direct analogues of the corresponding estimates for the AM and polarization. The proposed method of proof differs only by longer calculations in the theory of composites, but opens a wider perspective for studying a number of other problems in the theory of composites. Moreover, the exact value of the AM is calculated for two independently moving cylinders at the moment of contact.

MSC:

76B99 Incompressible inviscid fluids
74E30 Composite and mixture properties

Citations:

Zbl 0080.083
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References:

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