Blackwell Synergy

Submicrometer amplitude vibrations play an important role in different physical and engineering systems. Ultrasonic motors are typical examples of application of such vibrations. The vibration energy of piezoelectric ceramics is transferred to longitudinal or rotational motion of the elements of these motors.1-3 Experimental measurement of transverse vibrations of piezoceramics excited by an oscillating charge is a complicated technical challenge first of all due to the fact that the amplitudes of these oscillations are small. The problem gets even harder when the frequency of excitation is far from the resonance frequencies of piezoelectric ceramics.4 Pseudostatic (low frequency) excitation produces even smaller deformations of the piezoelectric ceramics. Nevertheless, the possibility of direct registration of transverse oscillations of electrically excited piezoceramics would be of great interest not only for the designers of ultrasonic motors5 but also for many others in different applications of piezoelectric materials.6,7 Atomic force microscopy (AFM) is effectively applied for the measurement of nanoscale displacement, strain, and thermal deformation fields.8-10 This paper is focused on the applicability of AFM for the measurement of dynamic displacements of electrically excited piezoelectric ceramic materials even far away from their resonance frequencies.

Plotting of moire fringes from the results of finite element calculations is important because of the ability of direct comparisons with the experimental results of analysis. The smooth variation of the intensity of the lines on the surface of the structure according to the trigonometric law is proposed. The method is applied to the visualisation of the inplane vibrations by stroboscopic photographing of the structure in the state of equilibrium and in the state of extreme deflections. Finally, the method is modified for the analysis of circular structures producing digital angular and radial moire fringes.