非均勻變截面梁(柱)自由振動(dòng)的差分法求解.pdf

1、蘭州理工大學(xué)碩士學(xué)位論文非均勻變截面梁（柱）自由振動(dòng)的差分法求解姓名：張立達(dá)申請學(xué)位級(jí)別：碩士專業(yè)：工程力學(xué)指導(dǎo)教師：李世榮20100501非均勻變截面梁自由振動(dòng)的差分法求解AbstractGenerallynonuniformbeamiswidelyusedinengineeringItisdifficulttoobtaintheanalyticalsolutionbecauseofthevariablecoefficientsoft

2、hedifferentialgoverningequationsNumericalmethodscanbeusedtogettheapproximatesolutionOnthebasisoftheEulerBernoullibeamtheoryfreevibrationofthenon—unifolTnbeamwithvariablecrosssection，subjectedtoaxialloadsandrested011theel

3、asticfoundation，isanalyzedbythefinitedifferencemethodNaturalfrequencyandmodeshapesaregivenTheeffectsofvariousparametersontheresponseofthevibrationarediscussedThemaincontentsofthisthesisareasfollow：1Byusingthecentraldiffe

4、renceschemeadiscretelinearalgebraicequation，withpentadiagonalcoefficientmatricesisobtainedfromanarbitraryfourth—orderordinarydifferentialequationThenbyusingtherecurrencemethod，therecurrenceformulaofthelinearalgebraicequa

5、tionsisobtainedBasedontherecurrenceformula，onlyfiveone—dimensionalarraysareusedtostorethecoefficientmatrixinthenumericalcalculationsTherefore，ithastheadvantageofbeingeasytoprogram，usingtheleaststoragespaceandhavinghighco

6、mputingspeedTheprogramofdifferencerecurrencesolutioninthisthesiscanbeusedtosolveallkindsoffourth—orderordinarydifferentialequationswithtwo—pointboundaryconditions2BasedontheEuler—Bernoullibeamtheorythefreevibrationofthen

7、on—uniformbeamswiththevariablecrosssection，subjectedtoaxialpressureandrestedontheelasticfoundation，isstudiedbytherecurrenceformulaofthefinitedifferencemethodIntheanalysis，thecross—sectionandelasticitymodulusofbeamareassu

8、medtobecontinuouschangeintheaxialdirectionThefreevibrationproblemofthefixedfixedandpined—pinedbeam，withvaryingcircularcross—section，subjectedtotheaxialpressureandrestedontheelasticfoundation，isresearchedrespectivelyasall

9、computingexampleThenon—dimensionalfrequenciesandthecorrespondingvibrationmodesofuniformcross—sectionbeamwithnoaxialpressureandelasticfoundationbythismethodareveryclosetotheclassicalanalyticalsolutionsTheeffectsofvariable