Vehicle Vibrations

Abstract

Vehicles are multiple-DOF systems as the one that is shown in Figure 13.1. The vibration behavior of a vehicle, which is called ride or ride comfort, is highly dependent on the natural frequencies and mode shapes of the vehicle. In this chapter, we review and examine the applied methods of determining the equations of motion, natural frequencies, and mode shapes of different models of vehicles. x ϕ θ FIGURE 13.1. A full car vibrating model of a vehicle. 13.1 Lagrange Method and Dissipation Function Lagrange equation, d dt µ ∂K ∂ ˙ q r ¶ − ∂K ∂q r = F r r = 1, 2, · · · n (13.1) or, d dt µ ∂L ∂ ˙ q r ¶ − ∂L ∂q r = Q r r = 1, 2, · · · n (13.2) as introduced in Equations (9.243) and (9.298), can both be applied to find the equations of motion for a vibrating system. However, for small and linear vibrations, we may use a simpler and more practical Lagrange