Thickness optimization of non-uniform beams based on modal shape

A new method for calculating bending vibration of a beam was proposed here.A calculating model for a non-uniform beam was established using finite difference method;the model could also be used for an uniform beam. Some examples showed that the model has good precision.Meanwhile,modal shape optimization was implemented to a non-uniform beam using the pre-established model.By changing the function's form of the model,it was possible to get the best thickness distribution to obtain an expected modal shape.An example showed that the proposed method is effective and applicable.