×

zbMATH — the first resource for mathematics

Plane waves in nonlocal micropolar elasticity. (English) Zbl 0564.73029
Dispersion relations are obtained for the transverse plane waves in linear, nonlocal micropolar elastic solids. By equating the frequency of the transverse acoustical (TA) branch at the end of the Brillouin zone, the nonlocal attenuation function is determined. The resulting (TA) curve for the frequency versus wave number \(\omega\) (k) fits well with the result known from the Born-Kármán theory of lattice dynamics, in the entire Brillouin zone. By using experimental values of \(\omega\) at the origin and the end of the Brillouin zone for Mg crystals, the micropolar elastic moduli are determined.

MSC:
74J20 Wave scattering in solid mechanics
82D25 Statistical mechanics of crystals
74A35 Polar materials
74J10 Bulk waves in solid mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cemal, Eringen A, Linear theory of nonlocal elasticity and dispersion of plane waves, Int. J. engrg. sci., 425-435, (1972) · Zbl 0241.73005
[2] Cemal, Eringen A, Nonlocal elasticity and waves, (), 81-105 · Zbl 0241.73005
[3] Eringen, A. Cemal, “On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves,” \( J. Applied Phys.\) (to appear). · Zbl 0326.73007
[4] Cemal, Eringen A; Speziale, C.G; Kim, B.S, Crack-tip problem in nonlocal elasticity, J. mech. phys. solid, 25, 339-355, (1977) · Zbl 0375.73083
[5] Cemal, Eringen A, Screw dislocation in nonlocal elasticity, J. phys. D., 10, 671-678, (1977) · Zbl 0357.73079
[6] Cemal, Eringen A, Line crack subject to shear, Int. J. of fracture, 14, 367-379, (1978)
[7] Eringen, A. Cemal, “Interaction of a Dislocation with a Crack,” \( J. Appl. Phys.\) (to appear). · Zbl 0326.73007
[8] Iyengar, P.K; Venkataraman, P.R; Vijayaraghavan; Roy, A.P, Dispersion relations for phonons in magnesium, (), 223-232
[9] Cemal, Eringen A, Nonlocal polar elastic continua, Int. J. engng. sci., 1-16, (1972) · Zbl 0229.73006
[10] Cemal, Eringen A, Linear theory of nonlocal microelasticity and dispersion of plane waves, Letters in appl. and-engng. sci., 129-146, (1973)
[11] Cemal, Eringen A, Nonlocal polar field theories, (), 205-267 · Zbl 1023.74003
[12] Cemal, Eringen A, A unified theory of thermomechanical materials, Int. J. engng. sci., 4, 179-202, (1966) · Zbl 0139.20204
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.