Traveling wave characteristics on two-dimensional finite structures using Hilbert transform

Abstract

In this study, we develop a method to analyze traveling waves generated by two bending modes of a two-dimensional piezoelectric actuator. This actuator has a composite structure constructed by a stainless-steel plate and piezoelectric PZT sheets. A developed analytical model analyzed the characteristics and efficiency of the traveling waves generated by the superposition of different bending modes. Using the multi-integer frequency, two-mode (MIF-TM) driving method, a steady traveling wave can be generated using two driving frequencies with an integer multiple relationships and near two bending modes. The optimization of the driving parameters is conducted by developing a cost function using the Hilbert transform, in which the driving voltages and the phase difference between the two driving frequencies are used. Finally, this analysis method is verified by using the finite element method.

Control of a multi-direction piezoelectric linear motor using a gyroscopic feedback control

“…Therefore, 1900Hz and 7600Hz were chosen as the two driving frequencies to maintain a 1:4 relationship. Since the wave numbers of Φ 21 and Φ 41 are 1:2 ratio, and the driving frequency ratio is even, the driving signals can be written as [9]:…”

“…(12). 𝐶 ̂ is determined by the ratio of time and space domain wavenumbers [9]. After obtaining the frequencies, phases, and voltage ratios between the two strings, the two rotating waves are superimposed and input to the 𝐴 1 , 𝐴 2 piezoelectric sheets.…”

“…Therefore, the signal for 𝐴 2 is a superposition of 𝐴 1 and 𝐴 3 signal. Referring to the optimization approach reported by Yang et al [9], the superposition of modes Φ 12 and Φ 21 can generate a steady linear traveling wave. The voltage is designed as in (15) with 𝐶 ̂= 1 .…”