杨氏模量数据处理(动态法)-2

用动态弯曲共振法测金属的杨氏模量数据处理

表格1次数质量M（g）棒长L（cm）直径d（mm）径长比：Δ仪uBuC123456平均标准差SuA74.9274.9574.9174.9274.9374.9174.9230.0150.00610.050.0290.0295118.03818.03618.03618.03618.03818.0418.0370.0020.00070.0020.0010.001337.9427.9397.947.9437.957.9467.9430.0040.00170.0050.0030.003330.044表格2支撑点距端点距离X（mm5101520X/L0.02780.05560.08330.111基频共振频率f0(hz)782.3778.8774.8771.6以X/L为横坐标，频率f0为纵坐标作图，在X/L=0.224处用内插法求出节点 位置的 f0 =共振频率768.6HZΔf仪=1HZ250.138771.1300.167769.4784f(Hz)350.194768.00.222768.550节点数0.250.2782769.1769.52X/L ——f图782780uc(f)uB(f)根据公式 130.577Hz778776774L3m2E1.60674fd7721.048E+11N/M2770768X/L76600.10.20.3表格3.d/LT0.021.0020.031.0050.041.0080.051.0140.061.0190.071.0260.081.0330.091.051由实际测得的径长比查表得修正系数经过修正的杨氏模量的公式为

E0=TE=

T=1.011.059E+11

N/m2

不确定度的计算:忽略修正值的不确定度,则

ur(E)uc(E)u(L)2u(m)2u(d)2u(f)29()()16()4()ELmdfuc(E)ur(E)E0.23%

2.4E+08

(1.059

±

N/m20.011)

E+11

N/m2

k=2

E=E0±U(E)=