内环向加筋对功能梯度圆柱壳模态频率的影响

Effects of inner ring-stiffener on modal frequencies of a functionally graded cylindrical shell

研究了内环向加筋功能梯度(functionally graded materials,FGMs)圆柱壳的模态频率。首先,运用Mori-Tanaka模型建立分离式和整体式加筋FGMs圆柱壳的材料属性;然后,基于三阶剪切变形理论推导了加筋FGMs圆柱壳自由振动的能量模型;在此基础上,结合圆柱壳的最小势能原理与Rayleigh-Ritz法,推导了加筋FGMs圆柱壳的模态频率方程,通过算例验证了模型的正确性和有效性;最后,探讨了加筋设计方式、加筋数量和加筋位置对圆柱壳模态频率的影响。结果表明:分离式加筋对温度的敏感性更弱,但有利于提高圆柱壳的模态频率;加筋数目对圆柱壳模态频率的影响具有收敛性;加筋的非均匀位置参数与圆柱壳几何参数存在相互匹配关系,对圆柱壳模态频率的影响较为复杂;加筋截面高度相比截面宽度,对圆柱壳模态频率更为敏感。

Modal frequencies of an inner ring-stiffened cylindrical shell made of functionally graded materials(FGMs)were studied in this article.Firstly,the Mori-Tanaka model was employed to obtain the material properties of the separated and integrated stiffened FGMs cylindrical shell.Thereafter,the energy model due to free vibration of the inner ring stiffened FGMs cylindrical shell was derived based the third-order shear deformation theory.Subsequently,the principle of minimum potential energy of the cylindrical shell and the Rayleigh-Ritz method were used to derive the modal frequency equation of the inner ring stiffened FGMs cylindrical shell.And the validity of the derived frequency model was verified by case studies.Lastly,the effects of the design method,the number of stiffeners,and the stiffener location of the cylindrical shell were discussed.Results indicate that the separated stiffeners are less sensitive to temperature,but are more advantage to increase the modal frequencies of a cylindrical shell.The effects of stiffener numbers on the modal frequencies of a cylindrical shell are converged.There is a matching relationship between the non-uniform position parameters of the stiffener and the geometric parameters of a cylindrical shell.The effects on the modal frequencies of a cylindrical shell are more complicated.The height of the stiffened section is more sensitive to the modal frequencies of a cylindrical shell than the width of the section.