Hi Does any one have any idea how to calculate the modal mass of the first mode of a clamped edge circular plate? I have tried doing it analytically but it has become impossible to integrate the mode function squared consisting Bessel Functions. Thanks.

I know a simple modal analysis in SolidWorks will give you the participative Modal Mass for each of the desired modes!

A web search turns up this paper, which also has references you can check out: Modal Mass of Clamped Beams and Clamped Plates Hope this helps.