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| Mechanical vibration not only produces noise but also trigs dynamic failure of material. Experientially, non-symmetric strain or stress is the main cause of instability of dynamic deformation. Based on geometrical field mechanics, it is found that, when the non-symmetric components of deformation are big enough, the vibration will become instable, which usually will trig the failure of material. The research shows that for a dynamic deformation the stress field is not symmetric even the deformation tensor is symmetric. However, for static deformation, the stress is always symmetric. This explains the non-linear behavior of vibration as the difference between the static deformation design with symmetric stress and the dynamic deformation with non-symmetrical stress. The vibration equation is introduced and discussed by finite geometrical field mechanics theory. Based on above results, the instability criteria for dynamic deformation are given in general form. The results will be applicable for the control of vibration. |
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| Keywords:vibration, deformation, motion equation, geometrical field |
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