In this paper we will analyse the most essential drawbacks of known solutions for the problem of vibrant infinite 1–D elastic lumped lines. We will present exact analytic solutions for forced and free vibrations of semi-infinite and infinite homogeneous elastic lines. We will analyse the solutions obtained, consider their physical essence and verify these solutions to corroborate they are exact and complete.
BazerJ., ‘Multiple scattering in one dimension’, J. Soc. Indust. Appl. Math., 12, 3, September 1964.
2.
GrigorievE. T.TultchinskayaN. B., ‘Joint longitudinal vibrations in inhomogeneous rods with systems of lumped masses elastically connected to them within a few sections’, Vibrations of complex mechanical systems. Transactions of Academy of Sciences of Ukraine. Institute of Technical Mechanics, Kyiv, Naukova Dumka, 1990, 144 pp. (Russian).
3.
PainH. J., The Physics of Vibrations and Waves, Moscow, Mir, 1979, 389 pp. (Russian; from the edition John Wiley and Sons, Ltd.London, New York, Sydney, Toronto, 1976).
4.
ElsgoltzL. E., Differential equations and calculus of variations. Moscow, Nauka, 1969, 424 pp. (Russian).
