According to the base frequency vibration of the rolling piston air conditioning compressor, the vibrating system mechanical model of compressor was established. By use of numerical calculation, a certain type of compressor vibration acceleration forecast was obtained with higher precision. The vibration system computer simulation model of compressor was built. The air conditioning compressor and its piping system vibration were predicted. This result was useful to the prediction and simulation of compressor, air conditioning system design and pipe optimization design.

The dynamic equation of a 2-dimentional hypersonic wing was derived by using the modified third order nonlinear piston theory. Both linear and nonlinear flutter boundary conditions were obtained through Hopf-bifurcation theory and directive numerical method respectively. The simulation results show that the effects of nonlinearities can delay or precede the appearance of limit cycles oscillations according to the system parameters.