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Flexural wave dispersion of nonlocal bi-Helmholtz-type stress gradient theory

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Abstract

In this study, harmonic wave propagation in elastic solid media is investigated. The accuracy of the proposed nonlocal bi-Helmholtz-type stress gradient theory with two nonlocal parameters is evaluated using dispersion curves and group velocity. The two nonlocal parameters are proposed as complex conjugate values. The group velocities are derived analytically and compared with Born–von Karman atomic lattice dynamics results. The wave dispersion curve and group velocity of the proposed nonlocal bi-Helmholtz-type stress gradient theory satisfy the Brillouin zone boundary criteria. It has been observed that the proposed theory shows better results in comparison with the general nonlocal theory. The proposed theory shows very close values with the lattice dynamics model. The nonlocal bi-Helmholtz-type stress gradient theory is in the generic form of nonlocal stress gradient theories. The other stress gradient theories based on nonlocal continuum elasticity are obtained as special cases of nonlocal bi-Helmholtz-type stress gradient theory.

https://doi.org/10.1177/1081286519897300

   Journal: Mathematics and Mechanics of Solids

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