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Proceeding from two-dimensional equation of motion of circular piezoelectric ceramic disks,withthe variables separated we can obtain a set of equations which depends only on the axial variable z.Then solving them with adjoint method according to the boundary conditions,the thickness vibrationalfrequency spectrum obtained is relative to the radial expansive frequencies.Conversely,from thefundamental frequency of thickness vibrations we can calculate the spectrum of radial expansive vibra-tions.From the result of calculations by this method,we can see that the radial and the axial vibrationspectra of circular piezoelectric disks are not only mutually influenced,but as well as dependent ontheir dielectric,piezoelectic,and elastic constants,that is to say“coupling”relations exist.
Proceeding from two-dimensional equation of motion of circular piezoelectric ceramic disks, with the variables separated we can obtain a set of equations which depends only on the axial variable z. Shen solving them with adjoint method according to the boundary conditions, the thickness vibrational frequency spectrum obtained is relative to the radial expansive frequencies. Conversely, from thefundamental frequency of thickness vibrations we can calculate the spectrum of radial expansive vibra-tions. From the result of calculations by this method, we can see that the radial and the axial vibrationspectra of circular piezoelectric disks are not only mutually influenced, but as well as dependent on their dielectric, piezoelectic, and elastic constants, that is to say “coupling ” relations exist.