Analysis of the resonance frequencies of multiple wheels–track coupled system based on the wave approach

Resonances of wheel and rail due to their interactions play an important role in the formation of irregular wear of wheel and rail profiles, which is the main cause of vibration and noise radiation from the wheel–rail interface and fatigue of vehicle and track structures. Although the concept of P2 resonance is widely known, other resonances due to the interaction of multiple wheels and rail above the cut-off frequency of the track system have not been studied in detail. Wave propagation in an infinite beam resting on an elastic foundation is formulated and solved analytically to illustrate the wave characteristics in railway tracks. The developed formulae can be applied to the Timoshenko beam or the Euler-Bernoulli beam with or without elastic support. The formation mechanisms and properties of the two resonance ranges of the multiple wheels–track coupled system are investigated. An important finding is the quasi-resonance frequency between 560 Hz and 610 Hz for various parameters of the vehicle and track systems, which has not been previously discovered in the literature. Although the resonances due to wave interaction are sensitive to axle spacing, the quasi-resonance frequency is independent of axle spacing. Once the resonance frequency induced by the wave interaction is close to the quasi-resonance frequency, significant resonance can be generated, which can contribute to the high-order polygonal wear of wheels as well as the short-pitch corrugation of rails. Both the model and the flexural wave solution provide a basis for more general investigation of vehicle–track interaction and other types of beams and attachments. The results can also provide guidelines for optimising of track and vehicle system to mitigate irregular wear of contact surfaces and the vibration and noise generated.