Equivalent Circuit Representation of a Flexurally Vibrating Bar with Axial Force

Abstract

The equivalent circuit for a flexurally vibrating thick bar with axial force is represented by impedance analogy. The effect of axial force is not represented as terminal pairs on the circuit, but is included in its matrix elements. It is shown that the resonant frequency equations under various end conditions can be easily obtained from the circuit. As an example, the resonant frequency change of the slender bar with both clamped ends by axial force was analyzed, and confirmed experimentally. The relationship between the change rate of the resonant frequency and axial force is linear. The value of the change rate for the first mode is larger than that for the second mode, and decreases as the thickness and width become larger. Moreover, the value increases with the length. These results will be utilized for the development and design of a force sensor based on the principle of the resonant frequency change by axial force.