惯性熵理论在横观各向同性圆柱壳中的应用

在横观各项同性圆柱壳热弹耦合的自由振动问题中应用惯性熵理论,引入3个位移函数将自由振动问题的方程简化为4个二阶常微分方程,用含复宗量的修正贝塞尔函数解得到位移、温度和应力的表达式.结合圆柱壳内外表面自由的边界条件,得到圆柱壳自由振动频率方程.选用锌作为介质,通过数值计算圆柱壳无量纲最低阶频率发现:中径与长度之比较大的圆柱壳中,其厚度的变化对自由振动最低阶频率的影响较大;轴向半波数较大的模态下,圆柱壳厚度对最低阶频率的影响相对较大;圆柱壳壁越薄,周向波数的影响越大;最低阶频率会随着周向波数的增大先减小而后增大;周向波数的增大会将圆柱壳厚度对频率的影响放大.研究表明,惯性熵理论可更方便用来解决热弹耦合动力问题.

Application of the Inertial Entropy Theory in Analysis of Transversely Isotropic Thermoelastic Cylindrical Shell

Abstract： The inertial entropy theory was used to analyze the thermoelastic coupling free vibration problem of a simply supported homogeneous transversely isotropic thermoelastic cylindrical shell. By introducing the displacement potential functions, the equations for free vibration problems could be reduced to four second order ordinary differential equations and modified Bessel function solutions with complex arguments could be obtained that can describe the displacement, temperature and stress. Considering the traction free and thermally insulated conditions at the lower and upper surfaces of the shell, the free vibration equation could be obtained. The crystal of Zinc was chosen as the material. The numerical calculations show that the thickness of the shell has a greater impact on the lowest frequency with the increase of mean radius to length ratio and the axial half full wave number. The circumferential full wave number has a greater impact on the lowest frequency of thinner wall shell. The lowest frequency decreases first and then increases with the ascent of the the circumferential full wave number. The increase of circumferential full wave number enlarges the influence of the thickness of the shell. The inertial entropy theory can get the exact solution with fewer parameters.