Vibrations of Elastic Strings: Mathematical Aspects, Part One

This paper is divided into two parts. Part One Chapter 1 contains the deduction of the model for vertical vibrations of elastic strings with moving ends and its relations to the models of d'Alembert and Kirchhoff-Carrier. Chapter 2 contains the results of investigations related to Kirchhoff-Carrier model during the last twenty years and an almost complete bibliography.Part Two Chapter 3 of the paper is dedicated to the model with moving ends. It contains new results obtained by the authors during the last five years.