This paper analyzes the forced transverse vibrations of an elastically connected double-string complex continuous system. The general solutions of forced vibrations of strings subjected to arbitrarily distributed continuous loads are found by using the method of expansion in a series of the mode shape functions. Di!erent cases of exciting loadings are analyzed. The action of stationary harmonic loads and moving concentrated forces is considered. Vibrations caused by the harmonic exciting forces are discussed, and conditions of resonance and dynamic vibration absorption are formulated. Thus the string-type dynamic absorber can be used to suppress the excessive vibrations of corresponding string systems. The dynamic string-type damper is a new concept of a continuous dynamic vibration absorber (CDVA). It is shown that a corresponding two-degree-of-freedom discrete system is an analogue of an elastically connected double-string complex system. Theoretical analysis is illustrated by a numerical example.
2000 Academic Press
Introduction
A companion paper [1] dealt with the free transverse vibrations of an elastically connected double-string complex continuous system. In this paper the forced transverse vibrations of the system are considered and the exact theoretical general solutions of the problem are formulated. The vibration problem of a two-string system has been analyzed by the author in other papers [2}5].
The vibration analysis of a double-string system can be helpful in the study of more complicated and di$cult double-beam system. This system has been investigated by many authors: Seelig and Hoppmann II [6,7], Kessel [8], Kessel and Raske [9], Saito and Chonan [10, 11], Kozlov [12], Kashin [13], Rao [14], Oniszczuk [15}25], Chonan [26, 27], Douglas and Yang [28], Stepanov [29], Dmitriyev [30], Hamada et al. [31, 32], Kokhmaniuk [33], Yankelevsky [34], Aida et al. [35], Kukla and Skalmierski [36], Chen and Sheu [37, 38], Chen et al. [39], Lueschen and Bergman [40], SzczesH niak [41, 42], Chen and Lin [43], and CabanH ska-P"aczkiewicz [44}46]. The present paper contains a more complete bibliography concerning the vibration problems of an elastically connected double-beam system.
FORCED VIBRATIONS
The transverse vibration problem of an elastically connected double-string complex continuous system is formulated in reference [1]. The model of a vibrating system is shown in Figure 1.