Bouncing of a Vehicle on an Irregularity: A Mathematical Model

Abstract

This paper leads with the phenomenon of the bouncing of a vehicle due to an irregularity being on a road or on a bridge deck. Attention is focused on the determination of the critical velocity for which the vehicle loses touch with the road's or the bridge-deck's surface following a missile's orbit and then striking the road or the bridge during landing. If the vehicle moves with a velocity greater than the critical one, we determine the corresponding time (and thus the point of the bridge) at which touch is lost. Afterwards, we determine also the landing point of the vehicle. Solving firstly the above problem for a vehicle moving on a road, it is easy next to proceed to the solution of the same problem for a vehicle moving on a bridge. The theoretical formulation is based on a continuous approach in addition to the use of a two degrees of freedom model associated with the mass of the moving load.

Irregularities and Roughness

“…The one actual load, is an idealized mass M, moving with constant speed υ (Figure 3 We assume also that the wheels are always in contact with the deck surface of the bridge while the speed υ is lower of both critical ones as they are determined in [22] .…”

“…Clearly, a closed form solution of equation ( 11d) is not possible. However, one can seek approximate solutions, based on previous pertinent works [22,23] .…”

“…The individual ones may have been structured to reduce the speed of the cars as they enter a bridge or for other traffic reasons. The form, the correct position and the lower and upper critical speeds (which are unique for each irregularity as a vehicle passes it) have been studied in detail [21,22] .…”

“…Kinds of moving loads The second actual load, is an idealized mass M, moving with constant speed υ, on a spring of constant ko and on a damper of constant co as it is shown in Figure 3 Model 2. Finally the vehicle's model used, is shown in Figure 3 Model 3.We assume also that the wheels are always in contact with the deck surface of the bridge while the speed υ is lower of both critical ones as they are determined in[22] .The studied bridges are of one span with length L, while are made of homogeneous and isotropic material with modulus of elasticity E, mass per unit length m and moment of inertia Iy. The damping coefficient cb is considered to be constant along the bridge.…”

Damaged-aircraft trailer dynamics simulation and vibration optimization

“…[4][5][6][7][8] A multi-axle heavy motorized wheel dump truck based on virtual and real prototype experiments integrating Kriging model is proposed in Gong et al, 9 but the approximate model doesn't contain tire and hydraulic parameters. In Michaltsos 10 a full mathematical vehicle model having 7 degrees of freedom (DOF) was developed. The transverse vibration of the bridge and the body bounce, pitch and roll of the vehicle are presented for different vehicle speeds, but optimization was not included in the research.…”