Dynamic Response of MDOF Structures. Equilibrium of forces condition gives the equations of motions:. Example : 2-DOF, identical mass & stiffness Free vibration. How do we solve this set of coupled equations?. By observation, the solution should be harmonic.
How do we solve this set of coupled equations?
Substituting into the equations of motion:
Need to find non-trivial solution coefficient matrix has to be singular
Natural frequencies motions:of the 2-DOF system.
Example motions:: 5-DOF, identical mass & stiffness Free vibration
Repeat the 2-DOF example motions:
Including damping motions:
find modes motions:
Mass-normalized modeshapes motions: