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本文叙述非接触的光学传感器应用于测定悬臂梁的弯曲共振频率及其标准振荡模的波形。一端夹于虎钳的悬臂梁所测得的共振频率的结果与伯努利—欧勒梁理论和铁摩辛哥梁理论相比较,虽然其振荡模波形与理论相符合,但是其随着细长比例数而变化的共振频率实验值与理论推导值之间存在着很大的差异。这类差异来源于夹持的不完善。结论是,如果要从测量悬臂梁的共振频率来计算精确的杨氏模量的话,试验必须限于细长的梁。对于不能制成这种形式的梁,提出了一种经验的方法使被试验的试样其杨氏模量值的误差为±3％。如果还需要提高精度,就需要用两端自由共振梁法。
This paper describes a non-contact optical sensor used to determine the bending resonant frequency of a cantilever beam and its standard oscillation mode waveform. Compared with the Bernoulli-Euler beam theory and the Timoshenko beam theory, the resonance frequency measured by the cantilever beam with one end clamped in the vise is consistent with the theory. However, There is a big difference between the experimental value of the resonant frequency and the theoretical deduced value, which varies with the number of long scales. This difference comes from the imperfect grip. The conclusion is that the test must be limited to an elongated beam if the exact Young’s modulus is to be calculated from the resonant frequency of the cantilever. For beams that can not be made in this form, an empirical method has been proposed to have a Young’s Modulus error of ± 3% for the specimens tested. If you also need to improve the accuracy, you need to use both ends of the free resonance beam method.