热环境下复杂边界环形板振动特性建模及分析

Modeling and Analysis of Vibration Characteristics of Complex Boundary Annular Plate Under Thermal Environment

提出一种统一的方法来预测环形板在稳态热环境下的自由振动行为。基于谱几何法(Spectral geometry method,SGM),采用改进的傅里叶级数展开环形板的位移。基于一阶剪切变形理论(First-order shear deformation theory,FSDT)得到了环形板的势能和最大动能。采用三组线性弹簧和一组旋转弹簧模拟环形板的任意边界,使用周向耦合弹簧以保证回转角为360°的圆环板周向边界的连续性,结合瑞利-里兹法构建环形板的理论模型,求解环形板的振动特性,通过与有限元(Finite element method,FEM)计算结果的对比,验证了该方法的准确性。本文采用无网格法,与目前主流的方法(如有限元法)相比,其计算效率更高。本文还研究了环形板的模态数值解和边界条件、内外半径比之间的关系。本文为环形板在工程实践中的应用提供了参考。

Annular plate structure is widely used in the engineering field.A unified method is proposed to predict the free vibration behavior of the annular plates in the steady-state thermal environment.Based on the spectral geometry method(SGM),the displacement of the annular plate is expanded by the improved Fourier series.The potential energy and the maximum kinetic energy of the annular plate are obtained based on the first-order shear deformation theory(FSDT).Three sets of linear springs and one set of rotating springs are used to simulate the arbitrary boundary of the annular plate.The continuity of the circumferential boundary of the annular plate with subtended angle of 360°is realized by using circumferential coupling spring.The Rayleigh-Ritz method is used to construct the theoretical model of the annular plate,and the vibration characteristics of the annular plate are solved.The accuracy of this method is verified by comparing with the finite element calculation results.The method used in this paper is a meshless method,which is more computationally efficient than current mainstream methods,such as the finite element method(FEM).The relationships between the modal numerical solution and boundary condition and the ratio of inner and outer radius in the thermal environment are studied.This paper provides a reference for the application of annular plates in engineering practice.