Design method of planar vibration system for specified ratio of energy peaks

The magnitudes of the resonant peaks should be considered in the design stage of any bandwidth-relevant applications to widen the working bandwidth. This paper presents a new design method for a planar vibration system that satisfies any desired ratio of peak magnitudes at target resonant frequencies. An important geometric property of a modal triangle formed from three vibration centers representing vibration modes is found. Utilizing the property, the analytical expressions for the vibration energy generated by external forces are derived in terms of the geometrical data of vibration centers. When any desired ratio of peak magnitudes is specified, the locations of the vibration centers are found from their analytical relations. The corresponding stiffness matrix can be determined and realized accordingly. The systematic design methods for direct- and base-excitation systems are developed, and one numerical example is presented to illustrate the proposed design method.