Mechanical equations of material damage and feature variation for vibration-based monitoring and diagnosis

Based on additive decomposition of deformation gradient tensor, the vibration equations for vibration-based damage monitoring and diagnosis technology are formulated with intrinsic local rotation concept. It shows that the abnormal vibration is related with asymmetrical stress (which is completely determined by the local rotation angular). Once the vibration velocity is well measured, the damage evolution equation can be used to determine the required damage evaluation parameter. Some further discussion is given out for the cracking tip wave features, which forms the basis for sound mission based monitoring technology. Material feature variation equations are also formulated. So, this research supplies the essential mechanical equations for vibration-based monitoring and diagnosis.