Vibration characteristics analysis of ring-stiffened conical shells based on power series method
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摘要:
目的 旨在利用解析法求解环肋圆锥壳的振动方程，对环肋圆锥壳的振动特性进行理论研究。 方法 首先，对圆锥壳分段处理，将圆锥壳沿母线方向、环向和法向的位移分别写成幂级数解的形式，并推导出幂级数项前系数的递推关系式； 然后，采用梁模型模拟不同环肋数对圆锥壳振动响应特性的影响；接着，将圆锥壳分段及其环肋边界条件、位移和内力矩阵进行组装求解，得到在外部简谐力激励下圆锥壳的振动响应特性，并将所得结果与ANSYS有限元数值方法的计算结果进行对比，验证所提计算方法的有效性。最后，运用所提理论方法进行环肋圆锥壳的振动特性分析。 结果 结果显示，圆锥壳安装的环肋可明显抑制圆锥壳的振动，具体表现为响应幅值降低、固有频率升高，且在相同频段内共振峰数量减小；增大壳体厚度会引起壳体振动响应幅值降低以及固有频率升高；此外，增大半锥角、轴线长度和环肋数均可降低环肋圆锥壳的振动响应幅值。 结论 研究表明，所用方法对环肋圆锥壳振动的理论研究具有一定意义。 Abstract:Objectives The purpose of this paper is to solve the vibration equations of a ring-stiffened conical shell using the analytical method, and to investigate the vibration characteristics of a ring-stiffened conical shell theoretically. Methods First, the ring-stiffened conical shell is processed in segments, and its displacement along the radial, circumferential and normal directions is written in the form of power series solutions respectively. The recurrence relations of the coefficients ahead of the power series are then derived in detail. At the same time, a beam model is used to simulate the influence of the number of ring-stiffeners on the vibration characteristics of the conical shell, and the boundary conditions, displacement, internal force matrices and ring-stiffeners of the conical shell segments are assembled and solved, thereby obtaining the vibration response of the shell under harmonic external excitation. Moreover, a comparison of the calculation results with those obtained by the ANSYS finite element analysis is carried out to verify the validity of the proposed method. Finally, the theoretical method is applied to analyze the vibration characteristics of the ring-stiffened conical shell theoretically. Results The results show that installing ring-stiffeners on the conical shell can significantly suppress the vibration of the conical shell, which is manifested by the decrease in response amplitude, the increase in natural frequency, and the decrease in the number of resonance peaks within the same frequency band. Increasing the thickness of the shell can reduce the vibration response amplitude and increase the natural frequency of the ring-stiffened conical shell. In addition, increasing the half cone angle, axis length and the number of ring ribs can also reduce the vibration response amplitude of the ring-stiffened conical shell. Conclusions The results of this study prove that the method used herein has a certain significance for the theoretical analysis of the vibration characteristics of ring-stiffened conical shells. -
图 2 环肋圆锥壳内力和力矩的方向关系图
Figure 2. Direction of internal forces and moments in the ring-stiffened conical shell
图 3 各阶轴向半波数下环肋圆锥壳振动的固有频率
Figure 3. Natural frequencies of the ring-stiffened conical shells under different number of axial half-waves
图 4 环肋圆锥壳的幅频响应曲线
Figure 4. Amplitude frequency response of the ring-stiffened conical shell
图 5 水平激励下环肋圆锥壳的幅频响应曲线
Figure 5. Amplitude frequency response of the ring-stiffened conical shell under horizontal excitation
图 6 环肋圆锥壳幅频响应的收敛曲线
Figure 6. The convergence curve of amplitude frequency response of the ring-stiffened conical shell
图 7 不同壳体厚度下环肋圆锥壳的幅频响应曲线
Figure 7. Amplitude frequency response of the ring-stiffened conical shell with different thickness of the shell
图 8 不同半锥角下环肋圆锥壳的幅频响应曲线
Figure 8. Amplitude frequency response of the ring-stiffened conical shell with different angles of semi-cone
图 9 不同轴线长度下环肋圆锥壳的幅频响应曲线
Figure 9. Amplitude frequency response of the ring-stiffened conical shell with different axis length
图 10 不同环肋数下环肋圆锥壳的幅频响应曲线
Figure 10. Amplitude frequency response of the ring-stiffened conical shell with different number of ribs
表 1 计算的环肋圆锥壳固有频率
Table 1. Calculated natural frequencies of the ring-stiffened conical shell
m n 不同方法计算的固有频率/Hz 偏差/% ANSYS 本文方法 1 1 86.762 85.833 −1.071 2 40.603 40.746 0.352 3 44.079 44.433 0.803 4 45.673 46.221 1.200 5 50.996 51.669 1.320 6 58.800 59.680 1.497 7 68.563 69.666 1.609 8 79.959 81.417 1.823 2 1 158.515 158.893 0.238 2 86.211 86.641 0.499 3 80.549 80.905 0.442 4 78.443 79.589 1.461 5 80.432 81.855 1.769 6 86.245 88.035 2.076 7 94.798 97.013 2.337 8 105.443 108.284 2.694 3 1 239.216 240.756 0.644 2 147.631 148.444 0.551 3 109.510 110.608 1.003 4 114.428 115.653 1.071 5 112.015 113.578 1.395 6 114.995 117.000 1.744 7 121.639 124.056 1.987 8 130.908 133.885 2.274 
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