where uðx; tÞ is the transversal displacement; V is the time-varying belt speed; c is the wave speed due to a
pretension in the belt; E is Young’s modulus; I is the moment of inertia with respect to the belt middle plane,
I ¼ L1h3
=12 (see Fig. 2); r is the mass density of the belt; A is the area of the belt cross-section, A ¼ L1h (see
Fig. 2); x is the space coordinate, and t is time.
The following simply supported boundary conditions are assumed: