Abstract：The deformations under different bolt pre-tightening forces and natural frequencies have been simulated by finite element analysis with ABAQUS. The natural frequency of the cylindrical resonator was also measured. The simulate results agreed very well with the experimental data which can be used to predict the shell motion perturbations and analyze resonant frequency of different modes.
［1］Mills I M, Mohr P J, Quinn T J, et al. Redefinition of Kilogram,ampere,Kelvin and mole: a proposed approach to implementing CIPM recommendation 1(C1-2005) ［J］. Metrologia,2006,43: 227-246.
［2］Moldover M R, Trusler J P M, Edwards T J, et al. Measurement of the universal gas constant using an acoustic resonator ［J］. Journal of Research of the National Institute of Standards and Technology, 1988,93: 85-144.
［3］Sutton G,Underwood R, Pitre L, et al. Acoustic resonator experiments at the triple point of water: First results for the Boltzmann constant and remaining challenges ［J］. International Journal of Thermophysics,2010,31:1310-1346.
［4］Pitre L, Sparasci F, Guillou A, et al. New determination of the Boltzmann constant with an acoustic method ［C］//Conference on Precision Electromagnetic Measurements,Korea,Daejeon,2010:129-130. ［
5］Gavioso R M, Benedetto, Albo P A G, et al. A determination of the Boltzmann constant from speed sound measurement in helium at a single thermodynamic state ［J］. Metrologia,2010,47: 387-409.
［6］Zhang J T, Lin H, et al. Cylindrical Acoustic Resonator for the Re-determination of Boltzmann Constant ［J］. International Journal of Thermophysics,2010,31:1273-1293.
［7］Zhang J T, Lin H, et al. Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator ［J］. International Journal of Thermophysics,2011,32: 1297-1329.
［8］Sun J P, Zhang J T, et al. Length Determination of a Fixed-Path Cylindrical Resonator with the Dual Wavelength Laser Interference Method ［J］. International Journal of Thermophysics,2011,32: 1330-1338.
［9］Mehl J B, et al. Spherical acoustic resonator: Effects of shell motion ［J］. Journal of the Acoustical Society of America,1985,78: 782-788.
［10］张凯,林鸿,等.等倾干涉法测量小孔径圆柱腔特征长度 ［J］.仪器仪表学报,2011,32: 2330-2335.
2015, Vol. 36 
