Random Vibrations of Strings; Longitudinal and Torsional Vibrations of Straight Rods

Abstract

It was considered in the preceding chapters devoted to random vibrations of mechanical systems with a finite number of degrees of freedom that elastic elements (for example, rod elements in Fig. 5.8, 5.9, 5.24, 6.7, 6.10) are inertialess, which, of course, is not quite so. This is true only in cases, where concentrated masses are considerably greater than the masses of elastic elements. Unfortunately, the term considerably greater does not relate to a specific numerical estimation and for this reason it is uncertain and sometimes unconvincing. Everything depends on the degree of accuracy imposed on the final numerical results of an analysis. For example, Figure 5.24 shows a concentrated mass m, connected with a spring that was considered massless (inertialess). The real spring, however, has a mass, which at vibrations leads to the occurence of inertia forces that can substantially change any calculation results obtained without regard to them.