To analyse a multi-degree of freedom (MDOF) system, the equation of motion should be constructed in the way that reflects the interaction between adjacent degree of freedom. Also, it is noticeable that for each degree of freedom, we will need to construct an equilibrium of motion. To be able to solve all their structural responses with ease, matrices is the best approach for us. By constructing such matrices for a 3-DOF system, we get to know their pattern and eventually, derive the general form of matrices representing the equation of motions.
The following shows the derivation of the equation of motion for MDOF system. Watch the video above for full details.
Idealization of SDOF and MDOF system
Derivation of equation of motion from 3-DOF system
General form of equation of motion for n-degree MDOF system
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