The laws governing the propagation, growth and decay of acceleration waves
in directed models of elastic beams are deduced for materials with zero and
non-zero heat flux, that is non-conductors and conductors of heat. The equ
ations depend explicitly on the geometric and inertial characteristic of th
e beam section and on the mechanical properties of the material. Solutions
are derived for the velocities of propagation and the evolution (amplitude
variation) of each type of wave (extension, bending, shear, twist). Results
are discussed and some numerical examples presented.