Problem 4.2 -- What smaller system(s) satisfy the same B.C.'s?
The previous page summarized some requirements for odd and even mode shapes.
Now, to analyze your symmetric system, you should:
Break the symmetric system down the middle into two "half-systems"
Model just one of the half-systems
Carefully identify the boundary conditions needed!!! Do this specifically to satisfy either odd or even mode shapes.
Don't forget any 'global' boundary conditions, if there were any.
Solve for modal frequencies (and any relative amplitudes of inertias and masses)
(...as done in problem 4.1)
Repeat for the other (odd or even) symmetry conditions (if applicable) to get the complete menu of modal shapes for your complete system.
When putting the sub-system mode shapes back together (to create mode shapes for the whole system), just remember your original relationships:
For an even mode:
For an odd mode:
(Except in a quiz) you can always use MATLAB to model your system and check your results. (See next page...)
