A mixed system of differential equations as a mathematical model of vibrations of continuum-discrete mechanical systems. (Russian) Zbl 1075.74546

Kul’terbaev, Kh. P.; Dzhankulaev, A. Ya.

Vladikavkaz. Mat. Zh. 3, No. 4, 28-35 (2001).

The authors study the spectral problem for a linear system of hyperbolic type coupled with a linear system of second-order ordinary differential equations arising in the context of mathematical modeling of continuum-discrete systems including a joint vibration of string and discrete system of bodies with finite degrees of freedom. In particular, a special attention is paid to determining spectra of the damping coefficients, the fundamental frequencies and eigensolutions in the presence of damping. The problem is solved numerically and is supplemented by a test example of vibration of a single string with fixed end points which shows adequacy of the mathematical model suggested. The authors note that comparison with measurements demonstrates a good agreement.

Reviewer: V. Grebenev (Novosibirsk)

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
74K05	Strings
70J50	Systems arising from the discretization of structural vibration problems

Keywords:

spectral problem; numerical investigation; string; damping