Abstract:
The flexural vibration equivalent circuit of a slender rod is derived based on the horizontal vibration equation and the electro-mechanical analogy. The electro-mechanical equivalent circuit of the slender rod with two slits is established by introducing the mechanical conversion coefficient between longitudinal and flexural vibration, and its resonance frequency equation is derived. By calculating the resonance frequencies of the rod with the different inclination angle slits in the longitudinal-flexural composite vibration mode using the equivalent circuit method (ECM) and the finite element method (FEM), the calculations show that, with the increase of the angle of the slits, the deviation of the resonance frequency calculated by the ECM and the FEM gradually increases, and when the angle of the slits is greater than 30°, the relative error between the two methods is more than 10%. The influence of the position, distance, length and inclined angle of the diagonal slits for the rod in its longitudinal-flexural composite vibration mode are analyzed by the FEM. It is found that when the distance between the two slits is 10 mm and the position of the slits is 30 mm from the input end of the rod, the rod has the best longitudinal-flexural composite vibration performance; with the increase of the length and the angle of the slits, the resonance frequency of the rod decreases and the ratio of the flexural displacement and the longitudinal displacement in the output end of the rod increases. The laser vibrometer is used to test the lateral and longitudinal vibration displacement of the ultrasonic vibration rod with two diagonal slits. The experimental results are basically the same as the simulation results.
