ABSTRACT
This chapter discusses longitudinal vibration in bars and focuses on the vibration of multidegree-of-freedom (MDOF) discrete systems. The governing equations for their motion can be easily formed using Newton's second law and can be analyzed by casting them into the eigenvalue form. Most practical systems have many degrees of freedom that are generally known as multidegree-of-freedom systems, MDOF systems for short. So it is important to understand the dynamics of these systems and to obtain their response to any arbitrary excitation. The main difference between an MDOF system and a single-degree-of-freedom (SDOF) system is that, in addition to natural frequencies corresponding to each degree of freedom, the degrees of freedom move in a characteristic manner corresponding to each natural frequency, known as mode shapes. Mode shapes play a very important role in the analysis of MDOF systems. Mode shapes represent relative displacement of each degree of freedom with respect to the other, corresponding to each natural frequency.
