Consider a railway car moving on a railroad track as shown in Fig. 8.36(a). The track can be modeled as an infinite beam resting on an elastic foundation and the car can be idealized as a moving load \(F_{0}(x, t)\) (see Fig. 8.36(b)). If the soil stiffness per unit length is \(k\), and the constant velocity of the car is \(v_{0}\), show that the equation of motion of the beam can be expressed as

\[E I \frac{\partial^{4} w(x, t)}{\partial x^{4}}+ho A \frac{\partial^{2} w(x, t)}{\partial t^{2}}+k w(x, t)=F_{0}\left(x-v_{0} t\right)\]

Indicate a method of solving the equation of motion if the moving load is assumed to be constant in magnitude.

Transcribed Image Text:

x=0 Fo(x, t) (a) 8888888888 000 Beam Vo 8888888- Soil stiffness (k) (b) FIGURE 8.36 Railway car moving on railroad track.