热环境中功能梯度圆柱壳的内共振非线性模态

摘要

研究热环境中无限长功能梯度薄壁圆柱壳内共振非线性模态，给出系统内共振条件；采用多尺度法建立系统具有内共振的非线性调谐方程；讨论梯度指数、温度变化及振动能量对系统非线性模态频响特性影响。研究表明，随调谐参数的变化，系统非线性模态会发生分岔；调谐参数分岔值取决于梯度指数、温度及振动能量。%Nonlinear normal modes of infinitely long functionally graded cylindrical thin shells with internal resonance in thermal environment were studied.The condition of internal resonance was obtained.The nonlinear modulation equations with internal resonance were established using the multiple scale method.The effects of gradient exponent,temperature and vibration energy on the frequency response characteristics of nonlinear normal modes were discussed.It is found that the nonlinear normal modes of system will undergo bifurcations with the variation of detuning parameter,and the bifurcation value of detuning parameter depends on the gradient exponent,temperature and vibration energy.