两种理论下梁振动固有频率试验研究

Experimental study on natural frequencies of beam vibration under two theories

现行弹性理论用梁弯曲正应力推导出了简支梁振动微分方程,并得出了梁的固有频率公式;而"非零应矩弹性理论"用梁弯曲弯应矩理论推导出了简支梁振动新的微分方程,并得出了新的梁固有频率计算公式。为对比两个固有频率的准确性,本文研究了通过简支梁跨中电机偏心转动施加不同频率的力,从而根据电机的转速确定简支梁发生共振时电机施加力的频率,即为简支梁的固有频率。试验结果:"非零应矩弹性理论"推导出的固有频率和其实测的共振时电机的频率基本一致,其误差都在0.16%~5.32%;而现行弹性理论推导出的固有频率与实测值的误差都在3.79%~43%。这证明了"非零应矩弹性理论"推导出的固有频率更准确。

The differential equation of forced vibration of beams with simply supported ends was put forward by using on the classical elasticity theory,then a natural frequency of beams could be obtained.The new differential equation of forced vibration of beams with simply supported ends was put forward by using on the non-zero bending point force moment elasticity theory,then a new natural frequency of beams could be obtained.In order to verify two natural frequencies of beams,a device to co-adjust eccentric moment of motor was installed at the center of beam.Resonance of beams could be obtained by adjusting motor speed.Comparisons motor frequency to two natural frequencies based on the different theories,the frequency closed to the motor frequency was the better.The experimental results show that the deviation of natural frequency using by the non-zero bending point force moment elasticity theory is within0.16%～5.32%,and the deviation of natural frequency using by the classical elasticity theory is within3.79%～43%.Thus,the validity of the natural frequency of the non-zero bending point force moment elasticity theory is confirmed.