Vibration modes in a string of three branches

D.A. VEGA; M.A. VILLAR; J.L. ALESSANDRINI; E.M. VALLÉS

JOURNAL OF SOUND AND VIBRATION

ACADEMIC PRESS LTD-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 1999 vol. 219 p. 920 - 924

0022-460X

The classic problem of the transverse vibrations of a string is of basic and technological interest, since it constitutes an acceptable model for the dynamic behavior of oceanographic cables and musical instruments among others. One of the important points in this area is the propagation of waves in systems with interferences or in mediums with different propagation speed. However, the literature shows, in general, very little information on the main aspects of stationary waves in these types of systems. In this work we studied the behavior of the transversal stationary waves in a mechanical system composed of three strings connected to a ramification point. First, the spectrum of natural frequencies of the system for a completely general case is presented. Then two particularly simple situations are studied: the case of a string with three identical branches and that of a string with two equal branches and the third of different length. Results obtained for a string with branches of different chain lengths are similar to those for a linear string of fixed ends in some particular situations.