A novel rapid positioning method for dynamic load location based on Newmark explicit method and modal shape comparison method

Accurately determining the location and magnitude of loads acting on a structure is crucial for structural design, optimization, and health monitoring. However, identifying the source of vibration through direct measurement is extremely challenging. Therefore, developing a rapid and accurate method for dynamic load location identification is essential. This paper focuses on proportionally damped continuous systems and proposes a novel and efficient method for dynamic load location identification. The traditional "response-system-load" framework for dynamic load identification is transformed into a "response-modal response-system-modal load" framework based on the Newmark explicit method, determining the modal loads of various orders in the vibration system. The modal shapes corresponding to the load location are then determined using the least squares inverse method, and the load location is identified by calculating the mode shape deviation function. Subsequently, an iterative strategy for dynamic load location identification is proposed to further enhance the computational efficiency of the method on complex structures. Simulated results demonstrate that, compared to the virtual load method, this method does not require load identification for every possible point, but only needs to identify modal loads once, significantly improving the speed of dynamic load location identification. Furthermore, the algorithm demonstrates high precision and excellent noise resistance in the identification of sinusoidal loads, broadband random loads, and impact loads. It also demonstrates robust adaptability under conditions of model uncertainties. To further verify the performance of the algorithm in practical applications, experimental studies on dynamic load identification were conducted on a simply supported beam system, and the results show that the algorithm is effective.