Effect of support position on the vibration-induced damage of frame structures

Determining optimal support positions is a simple and cost-effective method for vibration isolation, offering significant engineering and academic value. In this study, a novel wave model is developed through a wave-based vibration analysis method to investigate the vibration behavior of doubly supported beams and rectangular frames under Gaussian random excitation. The propagation, transmission, reflection, and connection mechanisms of elastic waves in two-dimensional structures are intuitively described using matrix representations to construct the wave equations of the system. Based on this framework, the distribution patterns of optimal support spans with respect to excitation frequency are revealed by solving the spatially averaged transmissibility ratio (Tr). Furthermore, the relationship between vibration damage and support positions under external excitations of different frequency ranges is explored. The results show that, compared to traditional models, the proposed model predicts optimal support positions that enable beams and frameworks to achieve more stable vibration suppression under high-frequency excitation, maintaining a vibration attenuation ratio of over 87 %. Both experimental and finite element simulation results align well with the predictions of this model.