圓板、環(huán)板和扇形板的自由振動和平衡問題的精確解.pdf

1、浙江大學博士學位論文圓板、環(huán)板和扇形板的自由振動和平衡問題的精確解姓名：徐榮橋申請學位級別：博士專業(yè)：固體力學指導教師：丁皓江陳偉球19990501苧壑：堡堡妻墮羔絲塑!生堡蘭塑塑塑璺竺墮苧壁—————————笪!壁!墮AbstractBasedonthefundamentalequationsofthree—dimensionaltheoryofelasticityandpiezoelectricitythestateequation

2、isderivedinthecaseofaxisymmetryThefiniteHankeltransformisthenemployedAftersubstitutingboundaryvariablesfortheinhomogeneousitemresultingfromthetransform，theordinarydifferentialequationswithconstantcoefficientsbecomehomoge

3、neousunderseveralkindsofboundaryconditionsWefinallyobtainSomethreedimensionalexactsolutionsforaxisymmetricfreevibrationandstaticequilibriumoflaminatedcircularandannularplatescomposedoftransverselyisotropicelasticandpiezo

4、electriclayersWealsoobtainthethree—dimensionalexactsolutionsforfreevibrationandstaticequilibriumofsectorialandsectorialannularplatesbyvirtueofgeneralsolutionsoftransverselyisotropicelasticityandpiezoelectricityrespective

5、lyThesesolutionscanbereducedtotheonesofcircularandannularplatesinthecaseofaxisymmetryandnonaxisymmetryInaddition，thesolutionsbasedontwodimensionalplatetheoriesarepresentedfortheboundaryconditionscorrespondingtotheaboveme