中文摘要：

圆柱声学共鸣法是测量Boltzmann常数和研究声学温度计的重要方法。热边界层和黏性边界层是影响圆柱声学共振频率的最主要因素。目前已有的声学一阶微扰理论已不能满足圆柱声学共鸣法精确测量Boltzmann常数的需求f不确定度小于1×10-6）。本文建立了基于声学二阶微扰理论的边界层扰动修正模型，计算结果表明，与一阶修正相比，二阶修正不影响圆柱声学腔的共振频率，但对频率半宽产生不可忽略的影响，且随着圆柱腔内的声学共振模式而变化，压力越低影响越大。对于长度80mm、半径40mm的圆柱腔，在273．16K、50kPa，二阶修正对Ar的（2,0，0）频率半宽的影响接近7×10-6。采用二阶修正模型，更符合真实物理规律，满足精确测量的需求。

英文摘要：

The acoustic cylindrical resonator method is one of the most importmant methods to determine the Boltzmann constant and acoustic thermometry. Thermal and viscous boundary layer cause the largest perturbation to the resonance frequecies. The corrections for the boundary layers based on the first-order theory are not sufficient for the Boltzmann constant determination towards 1×10-6 The second-order correction for cylindrical resonator is presented here. The calculation shows that the second-order correction doesn＇t have effects on the resonance frequencies, but have effects on the half-widths. At each temperature, the perturbation to the half-widths varies with the acoustic modes and increases with pressure p-1. For a cylindrical resonator with length of 80 mm and radius of 40 mm, at temperature of 273.16 K and pressure of 50 kPa in argon, the second-order correction to the half-width can be high up to 7× 10-6. The second-order correction leads to a better understanding of the energy loss in a cylindrical resonator.