VARIATION OF ENERGY AND PSEUDO-MOMENTUM IN ONE-DIMENSIONAL TRANSLATING CONTINUA
The energy source of instability is discussed for a one-dimensional translating (axially-moving) continuum. The speed of the translation is assumed constant. The energy equation and the balance of pseudo-momentum are derived that are in one-to-one correspondence with the linearized equation of transverse motion of the continuum. Based on these equations, it is shown that an external axial force has to act at every cross section of the continuum to maintain the kinematically prescribed translation. The work of this force, together with the energy flux through the end cross-sections of the continuum, determines whether the transverse motion of the continuum is stable or not.