Asymptotic analysis of kinematically excited dynamical systems near resonances. (English) Zbl 1348.70042
Summary: The dynamic response of a harmonically and kinematically excited spring pendulum is studied. This system is a multi-degree-of-freedom system and is considered as a good example for several engineering applications. The multiple-scale (MS) method allows us to analytically solve the equations of motion and recognize resonances. Also stability of the steady-state solutions can be verified. The transfer of energy from one to another mode of vibrations is illustrated.
MSC:
| 70H03 | Lagrange’s equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 70H14 | Stability problems for problems in Hamiltonian and Lagrangian mechanics |
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