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A mixed system of differential equations as a mathematical model of vibrations of continuum-discrete mechanical systems. (Russian) Zbl 1075.74546
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.
MSC:
74H45 Vibrations in dynamical problems in solid mechanics
74K05 Strings
70J50 Systems arising from the discretization of structural vibration problems
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