Does a beam fixed at one end and simply supported at the oth

Does a beam fixed at one end and simply supported at the other end, possess symmetric and anti symmetric modes? Why?

Solution

In the case of beams, symmetrical vibration modes will normally have a zero slope at the centre.For anti-symmetrical modes, the corresponding points on either side of the centre must have equal and opposite displacement. For any finite displacement at the centre would therefore cause a contradiction, which leads to the conclusion that there can be no displacement at the centre. Hence a beam fixed at one end and simply supported at the other end can possess symmetric and anti symmetric modes.