超声弯曲谐振杆计算的回归公式法和编表法

本文以解由 Timoshenko 杆理论得到的超越方程算得的弯曲振动杆谐振参数准确值为基准,采用多元回归分析方法得到用计算器即可方便地进行运算的计算谐振杆长和频率的回归公式,进而将其变换成可进行编表的形式,编制出设计用数据表。这些数据表可进行杆长、频率和杆截面尺寸计算。这两种方法在实用杆件范围内误差均不超过1%。对公式法和查表法均举了应用实例。并对几种算法和所得的结果作了比较。

Regression Formula Method and Compiling Databook Method for Exact Calculation of Ultrasonic Flexural Resonant Beams

In the present paper exact parameter values which are given from solving the transcendental equations based on Timoshenko beam theory are taken as standard data to perform polybasic regressive analysis.The regression formulas with which resonant length and frequency may be calculated with a calculator are found and transformed to the forms from which the databook for calculating the resonant length,frequency and the dimension of cross-section of the beams may be compiled,and then the databook are compiled.The error of calculating by above-mentioned methods are not more than 1%.The application examples of the methods are given. The features and the calculating results of the regression formula method, the compiling databook method and the classical one-dimensional theory method are compared.