Self-excited oscillators with asymmetric nonlinearities and one-to-two internal resonance
The authors study the dynamic behaviour of mechanical oscillators governed by the equations \(\ddot u_n+\omega^2_n u_n=f_n+ \varepsilon q_n(u_1,u_2, \dot u_1,\dot u_2)\), \((n=1,2)\), and involving quadratic nonlinearities. For small values of \(\varepsilon\), a first order solution is obtained by applying the multiple time scales method; then the stability properties of this solution are determined. As an example, the theory is applied to a simplified model of a metal cutting process, which is studied in details including comparison of numerical results with analytical ones.
scientific article; zbMATH DE number 1300045