Coupling mechanism analysis of structural modes and sound radiations of a tire tread band based on the S-mode technique

Abstract

Structural vibration is an important noise source for road tires. However, the generation mechanism of tire noise from vibration has not been so well understood because of the complicated coupling relations between vibrating modes and sound power radiations. In the present paper, sound power radiation of a vibrating tire tread band is investigated by a newly developed structure-dependent radiation mode (s-mode) technique. Differing from conventional acoustic radiation modes (a-modes) which are defined as a set of velocity distributions, s-modes are defined as a set of modal velocity distributions. Although both definitions allow the sound power to be described as a set of independently radiation terms, the s-mode description can set a direct relation between structural modes and s-modes for vibrating structures. Consequently, the s-mode technique can be very helpful on analyzing the coupling effects between the structural modes of a vibrating tire and its sound radiation. In the first instance, the tire tread band is modelled as a thin, cylindrical shell with both ends simply supported. In this case, complete analytical solutions are available for both structural modes and radiation modes of the model. Numerical investigations have shown that (1) each s-mode and the same ordered a-mode are associated with the same vibrating modes; (2) only low ordered radiation modes (either s-modes or a-modes) can radiate sound power efficiently into the surroundings within the frequency range of interest; (3) below the ring frequency, the dominant s-modes tend to be associated not only with the resonant modes, but also with the non-resonant modes whose nature frequencies are below the frequency of interest; (4) after the ring frequency, however, the sound power tends to be dominated by the vibrating modes which have natural frequencies nearby the frequency of interest, and at the same time, are associated with low axial wavenumbers.