Beams formed by long fiber composite materials have certain internal damping torque. A mathematical model for the displacement of this type of beams in cantilever configuration is the following initial-boundary value problem of an integro-differential equation [1, 14]:
where L is length of the beam, w(x, t) is the transverse displacement of the beam at time t and position x, ρ(x) is the mass density, EI is the stiffness parameter. The interaction integral kernel h(x, ξ) is introduced in this model by considering a restoring torque which comes from spatially variable bending of the beam. This kernel h(x, ξ) depends on the material properties of the beam. Choosing a different material (different h(x, ξ)) can realize a different damping effect for the beam.