Timoshenko梁自由振动分析及在称重仪中应用的研究

Analysis of Free Vibration of Timoshenko Beam and Study on Its Application in Weighing Instrument

称重仪主要是以应变片作为称重传感器进行测量,应变片贴在一根短粗的梁上。在称重过程中,梁产生振动,使得其测量时间延长。称重仪中的梁符合Timoshenko梁模型,由于Timoshenko悬臂梁自由振动理论模型的求解非常复杂,运用有限元法对称重仪的悬臂梁进行分析求解比较方便,运用其结果进行拟合,通过拟合的方程对梁的受力进行量纲一化,得到峭度指标,将梁的振动大小与峭度的对应关系应用于测量,缩短称重仪器检测时间。结果表明:采取峭度作为梁受力的量纲一化的指标,可快速确定梁的受力,测量的可靠性和合理性高。

The weighing instrument measures the weight mainly by the use of the strain foil as measuring transducer, which is at- tached to a stubby beam. The measured time is prolonged because of the beam vibration in the weighing process. The beam of weighing instrument was in accordance with the Timoshenko beam model, because the solution of theoretical model of free vibration of Timoshen- ko cant/lever beam was very complex, the analysis of cantilever beam of weighing instrument was taken by the finite element method （FEA） quite easy, and then which results were taken to curve fitting. Through the force of dimensionless according to the fitting equa- tion of beam, the index of Kurtosis was obtained. The corresponding relationship between Kurtosis and level of beam vibration was ap- plied to measurement, which shortened the time of measurement in weighing instrument. The results show that it can determine the beam stress quickly when taking kurtosis as dimensionless index which related to the beam force, the measurement is precise with high rationality.