A vibrating-tube ice sensor is developed to detect the ice in the complex situation automatically.In order to find out the vibrating characteristic of the tube

the wave equation is established based on the vibration theory

the general solution is obtained using the variable separation method

then

the fixed solution is obtained by integrating the simple structure model of the sensor and the detailed terms and conditions.After the fixed solution is simplified based on the magnitude computational algorithm

the mathematic model of the vibrating-tube ice sensor is established and three-order mode of axial vibrating are obtained.The sample test is carried out and the comparison between the results of test and calculation indicate that the mathematic model is valid and can be used in the structure design of the sensor.