Analytical and numerical investigations of the ultrasonic microprobe considering size effects.

In this article, dynamic behavior of vibratory microprobe is studied based on the strain gradient theory. The microprobe is considered as a piezoelectric actuator attached to a variable cross-section bar. The equation of motion is derived based on the strain gradient theory and solved both analytically and numerically. For analytical approach, a combination of mode summation and Galerkin's technique is used. Moreover, a hybrid finite element/finite difference method is used to calculate the numerical results. Findings show that there is an excellent agreement between the analytical and numerical results. Furthermore, the obtained natural frequencies and dynamic displacements of this work are compared with those of the classical theory and the effects of size dependency on the dynamic behavior of microprobe are discussed. [ABSTRACT FROM AUTHOR]