简支梁振台的理论解及位移测试

The Academic Solution and Deflection Test of Simple Beam Vibrator

利用由机械振动理论推导出的等截面简支梁的理论解,推导出了带集中质量的简支梁振动台的理论解,并通过分析动态条件下简支梁的位移与应变之间的关系,证明了:在动态条件下梁的位移与应变之间存在很好的正比关系。利用梁的位移与应变之间正比关系,如果在梁上适当位置粘贴应变片,通过测试应变就能准确地测得梁的动态位移。本文通过实例证明了该方法确实可行,理论解与实测结果非常吻合。这为简支梁的动态测试提供了有效而简便的方法。

The analytical solution of the simple beam with uniform cross section was concluded on the basis of the mechanical vibration theory; and furthermore the analytical solution of the simple beam vibrator with concentration mass was derived. Through analyzing the relationship between the deflection and the strain, it can be proved that the two quantities are in direct proportion for a simple beam under the dynamic condition. Based on the direct proportion relationship between the deflection and the strain, the dynamic deflection of the beam can be gained exactly through measuring the corresponding strain by affixing strain gages on proper places of the beam. The present method is proved appropriate and useful by the numerical results of an example, and the obtained results are fit for the testing order. Therefore the method is efficient and simple for dynamic tests of simple beams.