## 1 Introduction  
The suspension system of a vehicle is represented by the totality of rigid and elastic links between the chassis of a vehicle and the wheels, which allows for the relative motion between the two. In commercial vehicle designs, the main goal of the suspension system is to provide to the driver and passengers of the vehicle as much comfort as possible. This is usually achieved by limiting the amplitude of vertical accelerations experienced by the human occupants. In racing applications, however, the role of the suspension is to increase the performance envelope of the vehicle in order to have better dynamic results. The performance envelope of the vehicle is essentially a graphical representation of the maximum achievable lateral and longitudinal accelerations for a given velocity. By studying the performance envelope of a racing car, we can see that the maximum lateral and braking acceleration achievable are a function of the sum of all tire friction ellipses, while the forward acceleration of the vehicle is engine-limited. Another conclusion we can draw from the performance envelope is the fact that an increase of velocity will also increase the maximum achievable lateral and braking accelerations. This is a result of the fact that additional normal loads are added to the tires by the downforce generated at the higher traveling velocity. Given the fact that any increase of the performance envelope translates directly to better dynamic performances, two targets are set for the design engineer of a race car. The first target is the increase of the mechanical grip of the vehicle by improving the exploitation of the tire properties. The current engineering consensus when it comes to tire usage is that a minimization of the tire load variation [1] can be correlated with an overall increase in the grip provided. The second target of the design engineer must be the increase of the amount of downforce generated by the aerodynamic elements mounted on the vehicle. On a modern racing car, the majority of downforce (60-70%) is generated by the underbody of the car because it is usually designed to function as a venturi tunnel. However, the downforce generated by flow of air under the body is very sensitive to changes of the pitch angle. Studies done on IndyCar vehicles demonstrated that up to 50% can be lost if the pitch of the car changes just 1.3\({}^{\circ}\)[1]. Therefore, minimizing the pitch oscillation of the car is necessary to increase the aerodynamic grip. The vibration behavior of the vehicle describes how the wheels of the vehicle (the unsprung mass) oscillate relative to the chassis of the vehicle (the sprung mass). When considering a conventional vehicle with four wheels, this relative oscillation of the unsprung mass can be categorized into four natural modes of vibration. The bounce mode occurs when all the wheels of the vehicle oscillate in phase. The roll mode occurs when the wheels on the same side are in phase while the ones on the opposite side are in counter phase. The pitch mode occurs when the wheels at one end are in phase and the ones at the opposite ends are in counter phase. Finally, twist or wrap mode occurs when the diagonally opposed wheels are in phase [2]. All other combinations of wheel displacement can be described by a combination of these 4 modes. By looking at Figure 1, we can also see that the only nonplanar mode of vibration is the wrap mode. This kind of wheel oscillation relative to the sprung mass can only be excited by the road surface; therefore, any kind of stiffening for this mode will only increase the load variance of the wheel [3], with detrimental effects on the overall mechanical grip of the vehicle. Figure 1: Modes of vibration. (**a**) Bounce, (**b**) roll, (**c**) pitch, and (**d**) wrap. The discussion about the natural modes of vibration allows us to distinguish some shortcomings of the conventional suspension system.