含有初始缺陷双曲扁壳的固有振动特性分析
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摘要
以工程中常用的双曲壳结构如圆柱壳、球壳、双曲抛物壳为研究对象,利用薄扁壳理论,基于瑞利-里兹法和切比雪夫多项式求得了几种边界条件下的双曲扁壳的自由振动固有频率,并与ANSYS分析结果进行了对比,验证了该方法的适用性。详细研究了在不同边界条件下的双曲扁壳的几何参数、初始几何缺陷尺寸、初始几何缺陷密集程度对频率大小、频率转向、振型变化的影响。结果表明:随着壳体结构厚度的增加及曲率半径的减小,壳体的固有频率会增加;几何缺陷半波数及缺陷尺寸对频率影响情况较为复杂,并且会使系统发生频率转向问题,这些结果对于工程实际具有重要的理论指导意义。
Doubly curved shallow shell structures are widely used in the fields of machinery, aeronautics and architecture. It is well known that doubly curved shallow shells are unavoidable in manufacturing errors and initial geometric imperfections, at the same time, the study of different boundary conditions and different geometric parameters model can provide reference for engineering applications. In this paper, several special doubly curved shells including cylindrical shell, spherical and hyperbolic parabolic shells are taken as the research object; based on the thin shell theory and using the Rayleigh Ritz method and the Chebyshev polynomial, the natural frequencies under several boundary conditions are obtained. The results are compared with the ones of ANSYS; the applicability of the methods is verified. The effects of geometric parameters, initial geometric imperfection size and concentration degree on the frequencies, frequency steering and mode shifting under different boundary conditions are analyzed.
Doubly curved shallow shell structures are widely used in the fields of machinery, aeronautics and architecture. It is well known that doubly curved shallow shells are unavoidable in manufacturing errors and initial geometric imperfections, at the same time, the study of different boundary conditions and different geometric parameters model can provide reference for engineering applications. In this paper, several special doubly curved shells including cylindrical shell, spherical and hyperbolic parabolic shells are taken as the research object; based on the thin shell theory and using the Rayleigh Ritz method and the Chebyshev polynomial, the natural frequencies under several boundary conditions are obtained. The results are compared with the ones of ANSYS; the applicability of the methods is verified. The effects of geometric parameters, initial geometric imperfection size and concentration degree on the frequencies, frequency steering and mode shifting under different boundary conditions are analyzed.
引文
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[2]JIN G Y,SHI S X,SU Z.A modified Fourier-Ritz approach for free vibration analysis of laminated functionally graded shallow shells with general boundary conditions[J].International journal of mechanical sciences,2015,93:256-269.
[3]KURPA L,SHMATKO T,TIMCHENKO G.Free vibration analysis of laminated shallow shells with complex shape using the R-functions method[J].Composite structures,2010,93(1):225-233.
[4]XIE X,ZHENG H.Free vibration of four-parameter functionally graded spherical and parabolic shells of revolution with arbitrary boundary conditions[J].Composites part B engineering,2015,77:59-73.
[5]YE T G,JIN G Y.A unified Chebyshev-Ritz formulation for vibration analysis of composite laminated deep open shells with arbitrary boundary conditions[J].Archive of applied mechanics,2014,84(4):441-471.
[6]刘彦琦,褚福磊.几何参数对旋转薄壁圆柱壳振动特性的影响[J].振动与冲击,2012,31(13):22-25.(LIU Yanqi,CHU Fulei.Influence of geometric parameters on vibration characteristics of a rotating thin cylindrical shell[J].Journal of vibration and shock,2012,31(13):22-25(in Chinese)).
[7]孙述鹏.转动薄壁圆柱壳的动力学特性研究[D].哈尔滨:哈尔滨工业大学,2013.(SUN Shupeng.Study on dynamic characteristics of thin-walled cylindrical shells[D].Harbin:Harbin Institute of Technology,2013(in Chinese)).
[8]王宇.含初始几何缺陷悬臂薄板的动态特性分析[D].北京:北京信息科技大学,2017.(WANG Yu.Dynamic analysis of cantilever thin plate with initial geometric imperfections[D].Beijing:Beijing Information Science and Technology University,2017(in Chinese)).
[9]GUPTA A,TALHA M.Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shear and normal deformation theory[J].Composites part Bengineering,2017,123:241-261.
[10]AMABILI M.Nonlinear vibrations and stability of shells and plates[M].Cambridge:Cambridge University Press,2008.
[11]CAO D X,LIU B Y.Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers[J].Science China technological sciences,2017(11):1-15.