# Nonlinear Suppression of a Dual-Tube Coriolis Mass Flowmeter Based on Synchronization Effect
## 5 Conclusions and Prospects  
In this study, based on previous theoretical derivations and actual industrial demand, the effect of symmetric and asymmetric additional masses on the nonlinear frequency doubling of a coupling system was studied by introducing additional mass into the theoretical model. The effect of additional mass was further verified and explored through experiments. The final experimental and numerical analysis results were basically consistent; that is, the nonlinear frequency doubling phenomenon can be addressed based on industrial requirements from the two perspectives of low-frequency suppression and high-frequency suppression. A CMF can be specifically designed in accordance with the requirements for the working environment and measuring accuracy: for a CMF with higher measuring accuracy requirements for low frequencies, mass can be added on the beams  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{**Frequencies (Hz)**} & & & & & & & & & \\ \hline \multirow{8}{*}{Channel 1} & \multicolumn{2}{c}{Additional-} & \multicolumn{3}{c}{1 g} & \multicolumn{3}{c}{3 g} & \multicolumn{3}{c}{5 g} & \multicolumn{3}{c}{} \\ \cline{2-13}  & mass position & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) \\ \cline{2-13}  & \(l/2\) & 133.29 & 266.57 & 399.55 & - & 133.19 & 266.42 & 399.61 & - & 133.13 & 266.32 & 399.55 & - \\  & \(l\times 3/4\) & 133.10 & 266.16 & 399.26 & - & 132.81 & 265.66 & 398.47 & 531.32 & 132.56 & 265.15 & 397.72 & - \\  & \(l\) & 132.85 & 265.69 & 398.54 & - & 132.15 & 264.33 & 396.48 & - & 131.46 & 262.94 & 394.43 & 525.89 \\  & Ap & 132.91 & 265.85 & - & - & 132.34 & 264.49 & 396.80 & - & 131.65 & 263.32 & 395.00 & - \\ \hline \multirow{8}{*}{Channel 2} & \multicolumn{3}{c}{1 g} & \multicolumn{3}{c}{3 g} & \multicolumn{3}{c}{5 g} & \multicolumn{3}{c}{} \\ \cline{2-13}  & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) \\ \cline{2-13}  & \(l/2\) & 133.26 & 266.57 & - & - & 133.19 & 266.39 & 399.61 & 532.80 & 133.16 & 266.32 & 399.48 & 532.64 \\  & \(l\times 3/4\) & 132.94 & 265.79 & - & - & 132.81 & 265.66 & - & - & 132.59 & 265.19 & 397.75 & 530.34 \\  & \(l\) & 132.88 & 265.69 & - & - & 531.38 & 132.15 & 264.30 & - & 528.60 & 131.49 & 262.98 & 394.40 & 525.89 \\  & Ap & 132.91 & 265.82 & - & - & 132.31 & 264.68 & 396.80 & 529.14 & 131.71 & 263.32 & 395.03 & 526.68 \\ \hline \multirow{8}{*}{Channel 7} & \multicolumn{3}{c}{1 g} & \multicolumn{3}{c}{3 g} & \multicolumn{3}{c}{5 g} & \multicolumn{3}{c}{} \\ \cline{2-13}  & & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) \\ \cline{2-13}  & \(l/2\) & 133.29 & 266.57 & - & - &near or far from the base. For a CMF with higher measuring accuracy requirements for high frequencies, mass can be added at the far end of the beams, thus achieving high-frequency doubling suppression and improving the CMF performance. When the asymmetric additional masses were small, there was a certain suppression effect. However, as the additional mass increased, the suppression effect gradually became a frequency doubling phenomenon. Because of the natural frequency doubling phenomenon of the CMF, asymmetric additional mass can be easily overlooked. This meant that in industrial work, an asymmetry of the measuring tube mass resulting from pipeline appendages, pipeline wear, processing defects, etc. is easily detected only with a small mass. As the mass increases, the effect can be easily confused with the frequency doubling phenomenon of the CMF.