⋆ $$\bigstar $$ Two Degrees of Freedom Systems

There are many practical engineering situations where we model a vibrating system by attaching a secondary vibrating system to a primary system. The secondary system makes the whole system to have two degrees of freedom (DOFs) and affects the primary system, making it to deviate from its basic frequency responses of one-DOF systems. The harmonic excitation of the primary system can only be one of the following four types: 1. base excitation; 2. eccentric excitation; 3. eccentric base excitation; 4. forced excitation. In this chapter, we study the frequency response of these two-DOF systems from a design and practical viewpoint. The base excitation is the most practical model for vertical vibration of mechanical systems. The eccentric excitation is a model for equipment attached to a rotary motor on a suspension. The eccentric base excitation is a model for vibration of any double equipment mounted on an engine. While the forced excitation has almost no practical application, it is the simplest two-DOF forced vibrating system to serve as a good educational base. Vibration absorber is another topic that is connected to two-DOF systems. Consider a primary system of a mass supported by a spring. There is a harmonic force applied on the mass. We add a secondary vibrating system to absorb the vibrations of the primary. Adding a vibration absorber to a primary system generates a new system with 2 DOFs. The goal of having a vibration absorber is to design the suspension of the secondary system to reduce the amplitude of vibration of the mass of the primary at a given excitation frequency or in a range of frequencies.