Abstract: The initiation and development of the chaotic theory (modern nonlinear dynamics) and the significances of its applications in applied and engineering sciences are briefly described. Irregular vibrations in deterministic dynamic systems, one of the most significant achievements of modern science, in addition to the periodic and almost periodic vibrations are presented along with the developing history of chaotic theory. As the important topics of nonlinear science, the bifurcation theory and singularity theory are also introduced. Various nonlinearities encountered in the fields of practical engineering (including equipment manufacture, energy industry, transportation, construct industry, aviation and astronautics) are listed out. Research achievements on nonlinear dynamics of both large-scale rotational machine and vibrating machine (including the instability mechanism, bifurcation solutions, chaotic motions, fault diagnosis and its synthetic control techniques of the nonlinear rotor dynamical systems for large-scale rotating machinery, and the dynamic design strategy and nonlinear vibrations of large-scale resonant screens) are briefly presented. Hope the work mentioned above on the nonlinear dynamics of large-scale rotational machine and vibrating machine be benefited in further development of mechanical nonlinear dynamics in China, and also can be used as a theoretical support to the independent innovations of equipment manufacture in China.

Key words: Large-scale rotational machine, Mechanical dynamics, Nonlinear control technique, Nonlinear design technology, Significant vibrating fault