TRAVELING-WAVE ULTRASONIC MOTORS, .2. A NUMERICAL-METHOD FOR THE FLEXURAL VIBRATIONS OF THE STATOR

A finite difference scheme is used to calculate the forced transverse vibrations of thin annular plates with radially varying thickness. Under the assumption of harmonic motion, the governing partial differential equation reduces to a system of ordinary differential equations with variable coefficients. The numerical scheme that solves this system for various boundary conditions is successfully tested vs. known analytical solutions, and it is subsequently used to compute the forced vibrations of plates with more complicated thickness variations. The numerical results for these plates are compared to experimental results and found to be in good agreement. The effects of the rotatory inertias are studied and found to be important at high frequencies. © 1993 Academic Press LImited.