Analysis of transient waves in thin structures utilizing matched asymptotic expansions

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 approximatio ns of the 3-D dynamic equations of elasticity in the case of plates and she lls. 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 o f the quasi-front (the extensional wave front in the classical structural t heories), while the outer expansion is applicable near the loaded edge of t he structure. Three types of the quasi-front [the Poisson (elastic) quasi-f ront, the viscous quasi-front and the mixed quasi-front] are revealed.