On the Resonant Vibrations of Thick Barium Titanate Disks

Abstract

An optical interference technique employing illuminated multiple beam Fizeau fringes has been used to study the surface motion of barium titanate disks. In a properly polarized, accurately shaped cylindrical disk only normal modes having symmetry with respect to the axis and to the central plane are observed. A particular disk having radius/semithickness ratio (a/l) of 3.86 has been studied in some detail, and the displacement patterns for three important modes in the thickness resonance region have been accurately measured. Stress distributions for these three modes have been calculated from theory and these show that the wave motion is of a complex character in all three cases; this question is discussed in the light of elementary conceptions of thickness resonance. A more comprehensive experimental survey covering 25 different values of a/l within the range 1.14 to 6.63 has now been completed, and vibration patterns of 12 modes are given together with graphs of resonance frequency and values of electromechanical coupling coefficient. At relatively low frequencies the observed modes are obviously of the radial type but as the frequency approaches a value such that 2.5l = Λs where Λs is the wavelength of Rayleigh waves, take the form of a surface wave resonance with maximum motion occurring at the edge of the disk. There is no single mode which can be uniquely identified as the fundamental dilatational thickness resonance Rather, as a/l changes, each mode in turn passes through a maximum or minimum of electromechanical coupling the thickness resonance region. In general, for any given value of a/l two or three modes have high coupling this region, and the vibration patterns have certain well-defined forms but none approaches uniform piston-like motion. Nevertheless, there is some evidence suggesting an optimum value of a/l in transducer design.