f=(1/2π)√(k_t/.3m), where m is the mass of the transducer, and .3m is approximately the effective mass.

m=ρ_Ni t/2*l^2+ρ_PZT*t/2*l^2, assuming the width and length of the transducer are the same.

k_t=(E*t^3)/(4*l^2 ),E_PZT=63 GPa,E_Ni=200 GPa

1/k_total =2/k_Ni +1/k_PZT