“…It often brings many serious hazards in engineering, and is usually the direct cause of mechanical and structural damage and failure. For example, due to vibration, the machining accuracy of machine tools is reduced, maintenance costs are increased, electronic equipment cannot work properly, and vehicle frames fail and fracture ( Maia et al., 2003 ; Bin et al., 2018 ; Han et al., 2020 ). In addition, according to statistics, about 42% of total gas turbine failures have been caused because of vibration ( Meher-Homji, 1995 ).…”