Automatic assembly system has been continuously drawing attention since the beginning of the 20th century. Parts feeding system is one of the important subsystems. The parts feeding system is used for delivering bulk parts into separated individual parts. Flexible parts feeder gains attention because of the flexibility and the short changeover. However, due to the random vibration of the tooling plate in this parts feeder, the efficiency is low, especially for complicated geometry parts. Studies in this thesis are developments based on an industrial project to solve the problem of random vibration. The proposed approach is to make use of the standing waves created by the piezoelectric actuators on the tooling plate. Therefore, the investigation focus mainly on two aspects: resonance analysis and the mechanical interaction. With regard to resonance analysis, we firstly investigate the piezoelectric actuator's dimensions and the influence on the plate amplitude. We discover that bigger the piezoelectric actuator is, larger the vibrating amplitude is. We also find that for a piezoelectric actuator with a given surface, piezoelectric actuator's shape can be modified to increase the amplitude. The larger edge of the piezoelectric actuator should be orientated consistency with the bending direction. The limit of the dimension and shape modification is that the larger edge of the piezoelectric actuator should be smaller than the half wavelength of the resonant mode. Secondly, we study the plate geometry influence on the relative nodal lines position between modes. The length-to-width ratio changes the nodal line positions. We propose a parameter, which relates the relative distance between the nodal positions of two successive modes and the wavelength of the second mode, as the first step for plate optimization. With regard to the mechanical interaction, we firstly study the part's vertical displacement under a resonant vibrating plate. Numerical simulations, validated by experiments of the part's vertical displacement show that we can obtain a certain vertical displacement by either a high vibrating frequency with low amplitude or a lower frequency with higher amplitude. We also study the horizontal movement from anti-nodes to nodes. The established model considers the amplitude variation from anti-node to node. Part's vertical displacement is limited to small value to avoid parts' random movement. This leads to a slow horizontal movement. We apply the aforementioned researches to three applications. Firstly, for parts separation, two desirable standing waves are used to separate the parts. The two modes should satisfy this condition: the anti-nodes of the first mode are the nodes of the second mode and the nodes of the first mode are the anti-nodes of the second mode. The predicable positions (nodes) on the plate could be used to reduce the random vibration in the existing parts feeder. Secondly, a series of modes in a rectangular plate is obtained to transport the parts in one direction continuously. The desirable modes are obtained by adjusting the length-to-width ratio of the plate. A prototype is manufactured and used to transport the part in one direction. Thirdly, degenerated modes in the square plate are used to create quasi-travelling wave. Simulations and corresponding experiments are carried out.