As far as I know, natural frequency is the frequency of an object when it is in its natural position, e.g. unforced excitation. The equation governing it is , w(omega)=sqrt*(k/m) where w(omega) is the natural frequency, k is the coefficient of material stiffness and m is the mass of the object.

I had just started doing phd in advance material engineering and piezoelectricity. Its somehow related with some physic knowledge but I am not sure the gravity of it.