不同边界条件薄壁截锥壳的高阶振动特性研究

High order vibration characteristics of thin walled truncated conical shell under different boundary conditions

采用传递矩阵法研究了不同边界条件下薄壁截锥壳的高阶振动特性。基于Love壳体理论建立薄壁截锥壳振动微分方程,根据薄壁截锥壳子段间的状态向量,通过传递矩阵法得出整体传递矩阵,并用高精度的精细积分法计算固有频率,通过文献和有限元法进行验证,并分析了薄壁截锥壳在不同边界条件下的高阶振动特性。结果表明,不同边界条件下,采用传递矩阵法计算高阶固有频率与有限元法的计算结果基本一致。当轴向半波数增加时,频率明显增大;随着周向波数的增加,频率先减小后增大。固支-固支和简支-简支边界下在m=1和n=7处得到最小频率,固支-自由边界下在m=1和n=6处得到最小频率,三种边界下最小频率值分别为400.1、325.6和226.1 Hz;边界条件约束越多,最低阶固有频率越大。

The high-order vibration characteristics of a thin-walled truncated conical shell under different boundary conditions are studied by transfer matrix method.The vibration differential equation of the thin walled truncated conical shell is established based on love shell theory.According to the state vector between the sub segments of the thin-walled truncated conical shell,an overall transfer matrix is obtained by transfer matrix method,and the natural frequency is calculated by high-precision precise integration method.It is veri-fied by literature and finite element method,and the high-order vibration characteristics of the thin-walled truncated conical shell under different boundary conditions are analyzed.The results show that under different boundary conditions,the calculated higher-order natural frequencies by transfer matrix method are basically consistent with those by finite element method.When the axial half wave number increases,the frequency in-creases obviously.With the increase of circumferential wave number,the frequency first decreases and then in-creases.The minimum frequencies are obtained at m=1 and n=7 under the clamped-clamped and simply-sim-ply supported boundaries,and at m=1 and n=6 under the clamped-free boundary.The minimum frequencies under the three boundaries are 400.1,325.6,and 226.1 Hz,respectively.The more boundary condition con-straints,the greater the lowest order natural frequency.