پديد آورنده :
اكرااحمدثاني، سميه
عنوان :
بررسي ارتعاشات غير خطي و پديده دوشاخه شدگي در يك سيستم دو درجه آزادي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
طراحي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده مكانيك
صفحه شمار :
يازده،101ص.: مصور،جدول،نمودار﴿رنگي﴾
يادداشت :
ص.ع.به فارسي و انگليسي
استاد مشاور :
مهران مرادي
توصيفگر ها :
جاذب ارتعاشي , تشديد ثانويه , تشديد اوليه , روش مقياس زماني متعدد
تاريخ نمايه سازي :
12/12/92
استاد داور :
مصطفي غيور، رضا تيكني
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Nonlinear Vibrations and Bifurcation Analysis of a Two Degree of Freedom System Somayeh Ekra Ahmadsani s ekra@me iut ac ir Date of Submission 1 21 2014 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisors Hassan Nahvi hnahvi@cc iut ac irAbstract In nonlinear structural vibration analysis using the linear modeling may lead to wrong results To accuratelypredict vibration behavior of structures a complete mathematical modeling is necessary Most systems that areanalyzed by using linear mathematical models are in fact nonlinear systems Nonlinear characteristics of a systemmay cause behaviors in the response that linear modeling does not have the ability to predict and explain In thisthesis the nonlinear vibrations and stability of a two degree of freedom system consisting of the main system andan absorber is studied under external excitation The cases of simultaneous secondary and internal resonances and simultaneous primary and internal resonances are considered for the analysis The absorber is used to controlthe main system vibrations when subjected to an external excitation force The system springs and dampers haveboth linear and cubic nonlinear terms The governing equations of motion of the system are derived using theNewton s second law To solve the equations the method of multiple time scale MTS which is an approximatemethod suitable for solving nonlinear differential equations have been used By separating the secular terms thefrequency response equations of the system are obtained The effects of linear and nonlinear parameters of thesystem on the amplitude of the main system is investigated Stability analysis of the responses is performed bythe method of Andronov and Vitt and the saddle node bifurcation points are detected Also the domain of thedetuning parameter related to the three response zone is determined If the detuning parameter is selected in thisdomain the jump phenomenon occures in the response Moreover the possibility of existence of bifurcation phenomenon in the response is studied In this way atfirst the system equations of motion were expressed in dimensionless form Then by defining the state variables the equations are expressed in state space form These equations were solved by using the fourth order runge kutta method in Matlab software To perform bifurcation analysis a bifurcation parameter known as controlparameter should be choosen In this analysis dimensionless excitation frequency is determined as the controlparameter Bifurcation diagram is drawn in order to detect periodic and chaotic responses The Poincar mapdiagram phase plane diagram and time response are used at different control parameter vlues to distinguishperiodic quasi periodic and chaotic motions By using these diagrams the system parameters can be selectedsuch that the quasi periodic and chaotic responses do not occure Keywords Nonlinear vibrations Vibration absorber Multiple time scale method Superharmonic resonance Bifurcation
استاد مشاور :
مهران مرادي
استاد داور :
مصطفي غيور، رضا تيكني
