Complexity of string vibration estimated from a concept of entropy

Abstract

This paper describes the complexity of forced vibration of a flexible string, on the basis of the concept analogous to entropy, popular in thermodynamics and communication theory, which the authors have introduced for evaluating the complexity of a reverberant field in a recent paper. The entropy of string vibration is defined in terms of energy contribution of each normal mode in which the vibration is formulated, and is discussed in connection with the frequency components and location of a driving force and with transient characteristics by unit impulsive force. As a result, it is found that the entropy increases with an increase in frequency band width of the force and approaches infinity, and that although the driving point varies the entropy according to the band width, it tends to be raised when random excitation. Moreover, in the transient response of the string, the entropy is shown to decrease with time after the excitation. Thus, the entropy employed here well represents the degree of energy distribution to each mode, and within this meaning, seems to be fit for a measure of complexity of the string vibration.