A study of thin rod dynamical stability - Khalifeh , Hasan Mohammad (Latakia University Journal -Basic Sciences Series, 2019)
The stability loss mechanism is associated with the excitation of periodic longitudinal waves in the rod, arising from the sudden application of a load, which, in turn, leads to transverse parametric resonances. A longitudinal impact on a thin elastic rod, generating in it a periodic system of longitudinal waves, is considered. For certain values ​​of the parameters of the problem in the linear approximation, these waves generate parametric resonances, accompanied by an unlimited increase in the amplitude of transverse oscillations. To obtain finite amplitudes, we consider a quasilinear system, which takes into account the influence of transverse oscillations on the longitudinal. Earlier, this system was numerically solved by the Bubnov – Galerkin method. Here an approximate analytical solution of this system, based on two-scale expansions, is constructed