M E 4410 Lecture 7: Vibration Lect 7

• School: Wayne State University
• Department: Mechanical Engineering
• Course: M E 4410
• Professor: Raouf Ibrahim

Document Summary

While it is possible to simplify the dynamics of complex systems and model them by one-degree-of-freedom to describe their motion, there are times when such modeling is far from representing the real motion. Two or more generalized coordinates may be needed. Such systems have more than one degree-of-freedom and are referred to as multi-degree-of-freedom systems. Instead of having one resonant condition, there are more conditions whose number equals the number of degrees of freedom of the system. Each resonant condition has its own characteristic mode shape. The study of a two-degree-of-freedom system will enable us to understand the general principles in many degrees of freedom system. The principal differences between one and two degrees of freedom are more than the differences between two and ten degrees. These equations can be written in the matrix form: (3) Equations (2) or (3) are linear, coupled, homogeneous differential equations with constant coefficients. There are several ways of obtaining the solution.