Rotating systems are subject to external and internal excitations that cause undesirable vibrations, taking to degradation of the structural integrity of the system and the users health. In the industrial area, for example, the vibration attenuation can allow rotating systems to operate more efficiently and safely, providing less frequent periodic maintenance and avoiding expensive cost. In this context, the control of vibrations has been the object of concern of research centers and the specialized literature is full in proposals of solutions for this subject. This work presents a theoretical proposal of the mathematical modeling of a rotating machine containing shape memory alloy wires, whose purpose is to promote the damping of lateral vibrations caused by perturbation forces, mainly unbalance forces. This work intends to construct a theoretical knowledge, in a research area of restricted and relevant domain.