Experimental analysis of the structure-borne tyre/road noise due to road discontinuities

A modified complex modal testing technique for a rotating tire with a flexible ring model

“…In addition, the comparison also shows that the different responses are well synchronized. The frequency of the main spindle force oscillation corresponds to the first vertical tire resonance frequency [2]. The frequency contents of the vibration velocity at different points are found to be different from each other.…”

“…The φ c and ψ c are the modal vector and adjoint modal vector of the Eq. (1) and the modal vectors can be used to express the complex displacement vector p.…”

“…The forward and backward waves of a rotating ring are represented by the negative and positive frequencies [1,14]. Therefore, if the imaginary value of the K satisfies the condition (b o0), it implies that the forward wave has a larger magnitude in the negative frequency region, while the backward mode has a larger magnitude in the positive frequency region.…”

“…The dynamic characteristics of rolling tires have been widely studied in the literature by looking at modes and propagating waves [1][2][3]. Next to the natural frequencies and the damping values, the directivity of the propagation wave of each complex mode (forward and backward waves) is an important parameter for the understanding of the dynamic characteristics of rolling tires.…”

“…Furthermore, an accurate estimation of the complex mode shape itself is also of great importance [4]. However, the experimental setup needed to identify the mode shapes using conventional modal testing approaches is quite complex and expensive as many points should be measured on the rotating object [1,2]. For this reason, Lee [5][6][7] introduced a complex modal testing (CMT) approach for rotating machinery, which makes it possible to estimate the directivity of each wave with only two responses measured at different points and two forces applied at different locations.…”