第41卷第1期2024年2月文章编号：1000-4939(2024)01-0216-09应用力学学报ChineseJournalofAppliedMechanicsVol.41No.1Feb.2024弹性支撑功能梯度微圆柱壳模态频率的研究吕志鹏，刘文光，刘超（南昌航空大学航空制造工程学院,330063南昌）摘要：在建立弹性支撑功能梯度薄壁微圆柱壳模型的基础上，基于修正的偶应力理论和一阶剪切变形理论，推导了微圆柱壳的模态频率方程，讨论了弹性支撑、尺寸效应、温度梯度、材料组分指数、孔隙以及几何尺寸等参数对微圆柱壳模态频率的影响。结果表明：微尺度下，弹性刚度系数在0～10°N/m²范围内对微圆柱壳的模态频率基本无影响，剪切刚度系数在0~5×104N/m范围内对模态频率的影响较大，且增大剪切刚度系数有益于提高微圆柱壳的模态频率；由修正的偶应力理论得到的模态频率大于由经典连续体理论得到的模态频率；在弹性支撑和尺寸效应有无考虑的4种组合下,模态频率随温度梯度和微圆柱壳长度的增大而减小，随陶瓷体积分数指数的增大而增大，随孔隙体积分数和微圆柱壳厚度的变化规律不同；温度梯度对考虑尺寸效应或弹性基础的微圆柱壳模态频率影响较大，而孔隙调节具弹性支撑微圆柱壳的模态频率尤其显著。关键词：热环境；弹性支撑；功能梯度材料；微圆柱壳；模态频率中图分类号：V215.4Studyonmodalfrequencyofafunctionallygradedcylindrical(SchoolofAeronauticalManufacturingEngineering,NanchangHangkongUniversity,330063Nanchang,China)Abstract:Basedonafunctionallygradedthin-walledcylindricalmicroshellmodelwithelasticsupport,themodalfrequencyequationwasderivedbyusingthemodifiedcouplestresstheoryandthefirst-ordersheardeformationtheory.Theimpactsoftheelasticsupport,sizeeffect,temperaturegradient,materialcomponentindex,poreandgeometrydimensionsonthemodalfrequenciesofthecylindricalmicroshellwerestudied.ResultsindicatethattheimpactsofelasticstiffnesscoefficientonthemodalfrequenciescanbeneglectedintherangeofOto10'N/m',buttheshearstiffnesscoefficienthasagreatinfluenceonthemodalfrequenciesintherangeof0to5×10*N/m.Moreover,increasingtheshearstiffnesscoefficientisbeneficialtoincreasingthemodalfrequencies.Themodalfrequenciesobtainedbymodifiedcouplestresstheoryarelargerthanthoseobtainedbyclassicalcontinuumtheory.Withorwithoutelasticsupportands...
