The bifurcation solutions of resonant cases, including the main resonance, subharmonic resonance, superharmonic resonance and fractional resonance, are studied with the Liapunov-Schmidt method. The (α’,β’)-plane o...The bifurcation solutions of resonant cases, including the main resonance, subharmonic resonance, superharmonic resonance and fractional resonance, are studied with the Liapunov-Schmidt method. The (α’,β’)-plane of every resonant case divides into six open regions; all points inside any one of the six regions give topologically equivalent response diagrams. The boundary arcs separating these six regions are of two distinct types: five of them are of the normal codimension-1 and one is of infinite codimensions. The theoretical base of vibration, control of nonlinear systems is presented.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The bifurcation solutions of resonant cases, including the main resonance, subharmonic resonance, superharmonic resonance and fractional resonance, are studied with the Liapunov-Schmidt method. The (α’,β’)-plane of every resonant case divides into six open regions; all points inside any one of the six regions give topologically equivalent response diagrams. The boundary arcs separating these six regions are of two distinct types: five of them are of the normal codimension-1 and one is of infinite codimensions. The theoretical base of vibration, control of nonlinear systems is presented.
