In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dyna...In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.展开更多
The high aerodynamic noise induced by automotive air conditioning systems has important effects on the ride comfort, and the centrifugal fan is the largest noise source in these systems. It is very important to reduce...The high aerodynamic noise induced by automotive air conditioning systems has important effects on the ride comfort, and the centrifugal fan is the largest noise source in these systems. It is very important to reduce the aerodynamic noise generated by the centrifugal fan. The flow field and the sound field on the whole centrifugal fan configuration have been carried out using the computational fluid dynamics. Simulation results show that the sound pressure level near the outlet of the centrifugal fan is too high. Based on the relationship between flow characteristics and the aerodynamic noise, four parameters of the centrifugal fan, i.e., impeller blade＇s outlet angle 0, volute tongue＇s gap t, collector inclination angle fl, and rotating speed n, were selected as design variables and optimized using response surface methodology. While keeping the function of flow rate unchanged, the peak noise level is reduced by 8 dB or 10.8%. The noise level is satisfactorily reduced.展开更多
文摘In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.
基金Project(50975083) supported by the National Natural Science Foundation of ChinaProject(61075001) supported by China State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyProject(201-IV-068) supported by the Fundamental Research Funds for the Central Universities,China
文摘The high aerodynamic noise induced by automotive air conditioning systems has important effects on the ride comfort, and the centrifugal fan is the largest noise source in these systems. It is very important to reduce the aerodynamic noise generated by the centrifugal fan. The flow field and the sound field on the whole centrifugal fan configuration have been carried out using the computational fluid dynamics. Simulation results show that the sound pressure level near the outlet of the centrifugal fan is too high. Based on the relationship between flow characteristics and the aerodynamic noise, four parameters of the centrifugal fan, i.e., impeller blade＇s outlet angle 0, volute tongue＇s gap t, collector inclination angle fl, and rotating speed n, were selected as design variables and optimized using response surface methodology. While keeping the function of flow rate unchanged, the peak noise level is reduced by 8 dB or 10.8%. The noise level is satisfactorily reduced.
