Cross-modal vibration energy method for dynamic force identification

Abstract

Force identification is important in locating the vibration and noise sources of an operating machine. The forced vibration response of linearly vibrating structure is linear by definition. However, the energy distribution of linearly vibrating structures contains "coupled terms" in the modal decomposition of the response function. These coupled terms represent the cross-modal energy terms of a dynamic structure under forced vibration. In this research, it is proved analytically that certain cross-modal energy terms are highly correlated to the location of the external exciting force. Based on this finding, a new force localization method based on the cross-modal energy terms is developed, and a new index based on the suitably selected cross-modal energy terms to locate the force is developed. Numerical tests on beam structures under force excitation with different frequencies and locations have been carried out to test the effectiveness of the proposed force localization method. It is found that the proposed force localization method works well on vibrating beam structures even when random noise is taken into consideration. It is shown that the new method can identify the exciting force well. Experiments are done for verification of the proposed force localization method.