Contour Maps of 'Squishing' of an Automobile's Pneumatic Tyre @ Various Speeds: ...

[u/Frangifer]

... the horizontal (x) axis is distance along the circumference of the tyre, & the vertical (y) one is distance across the tyre, both being with respect to the centre of the patch of contact with the road. The three speeds are 0㎞/h=0mph , 90㎞/h≈56mph , & 216㎞/h≈134mph . The objective index marking-out the 'squishing' is Lagrangian or Eulerian vibrational energy density: the contours are of constant one-or-the-other - whichever is being depicted ... see annotations. Also, see the paper the figures are from - ie

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Analytical solution for bending vibration of a thin-walled cylinder rolling on a time-varying force

http://alain.lebot.chez.com/download/rsos12.pdf

^{¡¡ may download without prompting – PDF document – 1‧01㎆ !!}

by

A Le Bot & G Duval & P Klein & J Lelong

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- for fuller explication.

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①②③ Figure 3. Repartition of Lagrangian vibrational energy E_∂ near the moving point force at f = 200 Hz for various moving speeds. Isovalues of energy (i) and energy versus position along the horizontal line y = 0.16 (ii): (a) V = 0 km h⁻¹ , (b) V = 90 km h⁻¹ and (c) V = 216 km h⁻¹ .

④⑤⑥ Figure 4. Repartition of Eulerian vibrational energy E_d near the moving point force at f = 200 Hz for various moving speeds. Isovalues of energy (i) and energy versus position along the horizontal line y = 0.16 (ii): (a) V = 0 km h⁻¹ , (b) V = 90 km h⁻¹ and (c) V = 216 km h⁻¹ .

⑦⑧⑨ Figure 5. Repartition of Lagrangian vibrational energy E_∂ near the moving point force at f = 2000 Hz for various moving speeds. Isovalues of energy (i) and energy versus position along the horizontal line y = 0.16 (ii): (a) V = 0 km h⁻¹ , (b) V = 90 km h⁻¹ and (c) V = 216 km h⁻¹ .

⑩⑪⑫ Figure 6. Repartition of Eulerian vibrational energy E_d near the moving point force at f = 2000 Hz for various movingspeeds. Isovalues of energy (i) and energy versus position along the horizontal line y = 0.16 (ii). (a) V = 0 km h⁻¹ , (b) V = 90 km h⁻¹ and (c) V = 216 km h⁻¹ .

[u/Frangifer]

¡¡ ＣＯＲＲＩＧＥＮＤＵＭＮ !!

😱🙄

I made a slight error in explicating what the y-axis is: it's clearly distance across the tyre from one side to the other , rather than from the centre of the patch-of-contact , as it goes from 0 to width , rather than from -½width to +½width .