Effects of general structural stress on vibrational power flow

Vibrational power flow contains two types of information, namely, vibration velocity and structural internal force, and is an important parameter for measuring vibration level and transmission. Structures are often under stress because of the working environment. This stress changes the vibration velocity and internal force of the structure. As a result, this stress affects the power flow. In practical engineering, structural stress often has a complex distribution. However, earlier studies mainly focused on the overall uniformly distributed stress, which cannot be applied to practical engineering vibration problems. The finite element method can handle this problem, but has several shortcomings, such as the lack of a clear explanation of the essential relationship between structural stress and vibration, the complicated process of applying specific stress, and the large number of calculations. This study considers the effect of general structural stress and determines the dynamic equation of a structure undergoing stress. By utilizing the orthogonality of specific order modes to decouple, we obtain the power flow analytical solution, which can be applied to structures with arbitrary distributed stress. Finally, we calculate and analyze the effect of structural stress on a welding plate. Results show that structural stress has a more significant effect on power flow than velocity and inner force and should be taken into account when considering vibration prediction and reduction in practical engineering