| Popis: |
The dynamics of a nonlinear mechanical system with a rigid cubic force characteristic for vibration protection of a human operator is studied. A numerical modeling of a system similar to the Duffing equation for kinematic excitation is performed. To analyze the results, an improved method of spectral analysis based on the representation of the correlation function on a small time interval by a square polynomial was used. It has been established that in the pre-resonance and resonance regions, the general solution should consist of three components of the 1/3-order subharmonic, the fundamental harmonic and the third harmonic. In the resonance zone, only the 1/3-order subharmonic and the fundamental harmonic are important. The numerically constructed module of the transfer function of the system in absolute motion indicates the possibility of an amplitude jump, which is demonstrated in laboratory experiments. The most sensitive parameter is the acceleration of the object protected from vibration. Therefore, at the spectral power of the displacement acceleration, in addition to the main harmonic, the third harmonic is also distinguishable. When studying even simple nonlinear mechanical systems, it is necessary to use both approximate analytical and numerical methods, but in combination with spectral analysis. |
