بررسي ارتعاشات آزاد پيوسته استوانه اي ساخته شده از مواد با خواص تابعي ﴿FGM﴾ با در نظرگرفتن جابه جايي هاي اوليه، اثرات حرارتي و فشاري

چكيده انگليسي :

Free Vibration of Pre deflected Cylindrical FGM Shells Including Thermal and Pressure Effects Behrouz Mirshafiee behroozmirshafiy@yahoo com Date of Submission 2012 02 9 Department of Mechanical engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Hassan Nahvi hnahvi@cc iut ac irAbstractFree Vibration analysis of simply supported FG cylindrical shells for four boundary conditions isperformed Fist different methods for manufacturing FGM materials is discussed then shell theories arementioned including theories considering thickness shear stress and rotary iteria Zero radial displacementat both ends and four different sets of in plane boundary conditions based on Zero displacement or Zerotension are considered Material properties of ingredients are assumed to be temperature dependant andmetal and ceramic volume fractions are gradually changed in the thickness direction of the shell First staticanalysis is performed axial and radial displacements are determined To verify the thesis axial stress isincreased and buckling of the shell for one example is found and compared with buckling results and itshows satisfactory agreement The effects of static deflection due to thermal effects and internal pressure onthe dynamic response are investigated Distribution of temperature across the shell thickness is found fromsteady state heat conduction only in the thickness direction for two kind of FGM and different volumefractions the temperature distribution is shown The equations of motion are based on the Love s shelltheory and the von Karman Donnell type of kinematic nonlinearity Hamilton principle is used to derivestatic and dynamic equations of motion The total nonlinear equations are linearized by separating static anddynamic deflection Using exact solution solving two uncoupled equations iteration method is used to findaxial unknown stress static analysis is performed to determine the pre stressed and pre deflected stateinduced by the thermal and pressure loadings Since circumferential displacement is decoupled only axialand radial displacements are mentioned and then the equations of motion are solved by the Galerkin smethod The equations are discriticized based on comparison functions circumferential wave number andfrequency term The effects of circumferential wave number is considered and optimum value to minimizethe frequency is determined To solve the equations we use m number of axial wave number this gives of3m equation and related frequencies and modeshapes By increase of m we can find higher frequencieswhich were not calculated before Convergence of natural frequency by increase of axial wave number isinvestigated Axial Circumferential and radial frequencies are calculated To find the lowest frequency Modeshapes for minimum axial circumferential and radial frequencies are found and shows they satisfyboundry conditions To increased the code run time two different methods to find mass and stiffness matrixare presented How to apply extended Galerkin method for different Boundry conditions to find minimumnatural frequencies is mentioned Quantity of rotary inertia is evaluated for different thicknesses and due toits smallness it is ignored The effects of power law index and different geometrical parameters on thenatural frequencies and corresponding mode shapes for different circumferential wave number in a thermalenvironment are investigated Effects of temperature increase on decline of natural frequencies isinvestigated Effects of static deflection on the vibration behavior of the shell are also studied The studyshows the the effects of different geometries different kinds of FGM based on variation of metal ceramicfrom in to out surface and vice versa At the end conclusion and new proposals to continue the work arementioned Keywords Functionally graded material Cylindrical shells Free Vibration Pre deflection Thermal effects Internal pressure

ميرشفيعي، بهروز

بررسي ارتعاشات آزاد پيوسته استوانه اي ساخته شده از مواد با خواص تابعي ﴿FGM﴾ با در نظرگرفتن جابه جايي هاي اوليه، اثرات حرارتي و فشاري

ارتعاشات آزاد , فشار داخلي