Give short answers to the following questions What is coupli

Give short answers to the following questions: What is coupling in a set of eqautions of motion for a TDOF system? Does coupling in equations of motion have any physical meaning? Why? Will coupling necessarily happen in equations of motion of a TDOF system? If not, when will the equations of motion to be-uncoupled? Will coupling change the natural frequencies? Why? Will coupling change the mode shapes? Why? Can the natural frequency be zero? Why?

Solution

i.

Coupling in a set of equations of motion for a TDOF system is a means to represent the motion of the same system with the use of generalized coordinate systems. While usinf these coordinates, the mass of stiffness matrices may be coupled or uncoupled. When the mass matrix is coupled, the system is said to be dynamically coupled and when the stiffness matrix is coupled, the system is said to be statically coupled.

ii.

Yes, the coupling in equations of motion have a physical meaning. During vibration tests, modal modes are excited enabling modal frequencies and modal shapes to be observed and estimated. Any coupled mathematical model based on mass, stiffness, damping properties and coupling stiffness forces have a physical meaning.