Fig. 1 The geometrical model of a circumferential groove is shown on the left. The first and the second acoustic resonances are represented on the right. More about this image found in The geometrical model of a circumferential groove is shown on the left. The...

Fig. 2 Inclusion of the lateral grooves with open ends and their effect on the acoustic mode shapes and natural frequencies. More about this image found in Inclusion of the lateral grooves with open ends and their effect on the aco...

Fig. 3 Effect of lateral grooves with closed ends (represented as black terminations) on the mode shapes and natural frequencies. More about this image found in Effect of lateral grooves with closed ends (represented as black terminatio...

Fig. 4 Effect of the lateral grooves' length on the resonance frequencies. On the left, the effect of open-end lateral grooves; on the right, closed-end grooves. Each marker represents a simulation result. More about this image found in Effect of the lateral grooves' length on the resonance frequencies. On the ...

Fig. 5 Effect of the number of lateral grooves on the resonance frequencies, considering open-end or closed-end lateral grooves. More about this image found in Effect of the number of lateral grooves on the resonance frequencies, consi...

Fig. 6 Effect on the resonances of different positions of the lateral grooves, considering a progressive shift of fractions of a pitch dimension (25 mm for this model). More about this image found in Effect on the resonances of different positions of the lateral grooves, con...

Fig. 7 Model for investigating the acoustic resonances of a tread pattern based on Approach 1. More about this image found in Model for investigating the acoustic resonances of a tread pattern based on...

Fig. 8 Modes with lowest frequencies, computed using Approach 1. These results are all part of the mode family ( 1 , m ) . A detail of the pressure variation inside a sipe is shown for the last resonance. More about this image found in Modes with lowest frequencies, computed using Approach 1. These results are...

Fig. 9 The acoustic model based on Approach 2. The geometry of the deformed treaded tire in contact with the drum is represented on the left. A detail of the footprint region is shown on the right. More about this image found in The acoustic model based on Approach 2. The geometry of the deformed treade...

Fig. 10 Mode shapes and natural frequencies of the mode family ( 1 , m ) evaluated using Approach 2. More about this image found in Mode shapes and natural frequencies of the mode family ( 1 , m ) ...

Fig. 11 In Approaches 3a and 3b, the footprint geometry is schematized as a network of mono-dimensional finite elements. Different colors are used to represent different cross-sectional areas. More about this image found in In Approaches 3a and 3b, the footprint geometry is schematized as a network...

Fig. 12 Mode shapes and natural frequencies evaluated using Approach 3b. More about this image found in Mode shapes and natural frequencies evaluated using Approach 3b.

Fig. 1 Infinite metamaterial plate: ( a ) full view of a metamaterial plate cell, ( b ) side view of the metaplate cell, ( c ) discretized view of a single periodic metaplate cell, and ( d ) periodic metamaterial plate of n th cells. More about this image found in Infinite metamaterial plate: ( a ) full view of a metamaterial plate cell, ...

Fig. 1 Infinite metamaterial plate: ( a ) full view of a metamaterial plate cell, ( b ) side view of the metaplate cell, ( c ) discretized view of a single periodic metaplate cell, and ( d ) periodic metamaterial plate of n th cells. More about this image found in Infinite metamaterial plate: ( a ) full view of a metamaterial plate cell, ...

Fig. 2 Metamaterial plate cell dispersion surfaces More about this image found in Metamaterial plate cell dispersion surfaces

Fig. 3 Metamaterial plate stopbands with ( a ) equal submasses, ( b ) unequal submasses. Nonsolid horizontal lines represent the lower and upper bounds of the corresponding second stopband at the overlap zone. More about this image found in Metamaterial plate stopbands with ( a ) equal submasses, ( b ) unequal subm...