Free vibrations of a tire as a toroidal membrane

Tyre/road interaction noise—A 3D viscoelastic multilayer model of a tyre belt

“…Some previous work has been based on finite element models of the tyre, which are best suited to analysis of lower frequency ranges, or for use at single frequencies of interest due to computational demands, see for example the work of Takahashi [4], Saigal [5] or Pietrzyk [6]. Other mathematical models have determined the vibration of the tyre belt using simplifications to obtain shell, ring and flat bending plate models such as the one developed by Kropp [7] [8].…”

In-plane surface modes of an elastic toroidal membrane

“…While the flexural family of modes depend predominantly on the prestress, the later two families of modes are found to be insensitive to prestress. The numerical analysis of vibrations of an inflated toroidal membrane in the context of tire dynamics has been reported by Saigal, Yang, Kim, and Soedel (1986). Approximate free vibration solution neglecting the curvature of the membrane for tires of small cross-section compared to the radius has also been obtained.…”

Parameter estimation of butyl rubber aided with dynamic mechanical analysis for numerical modelling of an air-inflated torus and experimental validation using 3D-laser Doppler vibrometer

“…19 Another work on obtaining the closed-form solution for the natural frequencies and mode shapes of a prestressed toroidal as a first approximation of the free vibration response of a tire was explored. 20 Touching on practical applications of the inflatable torus, an inflatable antenna experiment by National Aeronautics and Space Administration was launched on May 19, 1966. The mylar-made antenna was properly inflated and re-entered earth's atmosphere three days later.…”

“…19 Another work on obtaining the closed-form solution for the natural frequencies and mode shapes of a prestressed toroidal as a first approximation of the free vibration response of a tire was explored. 20…”