Summary
Transient extensional waves in thin structures are analyzed. The structure motion is governed by the Love theory in the case of rods and the theories with modified inertia corresponding to higher order asymptotic approximations of the 3-D dynamic equations of elasticity in the case of plates and shells. The effect of a small viscosity is involved on the basis of the Voigt model. The asymptotic technique utilizing matched expansions is developed. The inner (boundary layer) expansion is applicable in the narrow vicinity of the quasi-front (the extensional wave front in the classical structural theories), while the outer expansion is applicable near the loaded edge of the structure. Three types of the quasi-front [the Poisson (elastic) quasi-front, the viscous quasi-front and the mixed quasi-front] are revealed.
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Emri, I., Kaplunov, J.D. & Nolde, E.V. Analysis of transient waves in thin structures utilizing matched asymptotic expansions. Acta Mechanica 149, 55–68 (2001). https://doi.org/10.1007/BF01261663
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DOI: https://doi.org/10.1007/BF01261663