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Vibration of Circular Plates

Vibration of Circular Plates

Dear All,
These days I am do some research on vibration of circular plates (out-of-plane and in-plane). In the reference, the displacement in radial direction can be expressed with Bessel polynomial. I want to use the Rayleigh-Ritz method to solve these problems. The strain energy and kinetic energy can obtain with integral. If there is the bessel function, how to calculate the integral. Also I want to consider some spring in the boundary to change the boundary conditions.

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