5.1 Introduction

The problem was considered for a long time. But generally only static problems or problems involving nearly quasi static conditions were studied (various cables existing in applications). Rubber cables or synthetic strings are elongating very much when impacted, even with quite small forces. But in some modern textile machines the speed of operation is quite high (knitting, weaving, sewing, carding machines). Also in elastic cables used to break airplanes on ships, the speed is quite high. In dynamic problems the cables are influenced what concerns the yield limit, the work-hardening modulus, the breaking stress and the elastic modulus.

Impact velocities of the order of some hundred meters per second or even a few kilometers per second, when the component of the impact velocity ranges between the velocities of propagation of transverse and longitudinal waves, occur less often in practice and lead to difficult mathematical problems, as will be pointed out below. One must also take into account that textile materials cannot resist transverse impacts if the latter exceed a certain limit; for each textile yarn there is a certain limiting transverse impact velocity which at once breaks the string at the point of impact. These limiting velocities, generally, of the order of many hundred meters per second.

From the mechanical point of view, that is the simplest problem in which two kind of waves propagate and reflect together, influencing one another at every moment. This motion can be studied both experimentally and theoretically, because both kinds of wave...