i was doing free and forced vibration analysis of a cracked cantilever beam for different cases. i started with free vibration analysis. i want to find the natural frequency for the following cases.
even though we are not applying any force in case of free vibration analysis, practically we have to give an initial excitation.So here case a and c will behave differently,(because in case a since crack is on the same face of initial excitation it will try to expand the crack and in case of C it will contract the crack). but while not considering the direction of excitation there is no difference between case a and c( just an inverted image) , but in the paper i am referring he got different natural frequencies for the two cases, so can anyone help me to find the natural frequencies for cases a and C