بررسي ارتعاشات غير خطي و پديده دوشاخه اي شدن تير ويسكوالاستيك منحرك در راستاي محور

چكيده انگليسي :

Nonlinear Vibration and Bifurcation Analysis of Axially Moving Viscoelastic Beam Davood Gharloghi d gharloghi@me iut ac ir 22th January 2013 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Hassan Nahvi hnahvi@cc iut ac ir Abstract Vibrations are a part of our environment and daily life Many real life engineering devices such as band saws power transmission chains aerial cableways and serpentine belts involve transverse vibration of axially moving beams Despite its wide applications these devices suffer from the occurrence of large transverse vibrations due to initial excitations Transverse vibrations of these devices have been investigated to avoid possible fatigue failure and low quality operation For example vibration of the blade of band saws causes poor cutting quality Vibration of the belt leads to noise and accelerated wear of the belt in belt drive systems Therefore vibration analysis of axially moving beams is important for the design of devices In this work free nonlinear vibrations and nonlinear vibrations under weak and strong external excitations of axially moving viscoelastic Rayleigh beams with cubic nonlinearity are analyzed The governing partial differential equation of motion for large amplitude vibration is derived using Newton s second law and Hamilton principle through geometrical constitutive and dynamical relations For the beam material two parameter rheological model Kelvin Voiget has been considered By directly applying the method of multiple scales to the governing equations of motion and considering the solvability condition the linear and non linear frequencies and mode shapes of the system are analytically formulated Multiple time scale method is a type of perturbation method This method is suitable for solving weakly nonlinear problems Unlike multiple time scale method in direct multiple time scale method the mode shape and natural frequency is obtained exactly In higher order schemes and for finite mode truncations the direct perturbation method yields better approximations to the real problem The frequency equation is solved by applying the Newton Raphson method for optimization of a multi objective function Then the method of direct multiple time scales is employed to investigate primary resonances superharmonic resonances and subharmonic resonances of the problem Finally stability and bifurcation analysis are performed with applying the Routh Hurwitz criterion and considering eigenvalues of the Jacobian matrix In the presence of damping terms it can be seen that unlike an elastic beam the amplitude is exponentially time dependent and as a result the non linear natural frequencies of the system will be time dependent The numerical results show that natural frequency obtained for a Rayleigh beam is smaller than for an Euler Bernoulli beam The nonlinear natural frequency begins far from the linear one and then approaches towards it For the system with small viscosity factor values the nonlinear natural frequency approaches the linear one more smoothly than those which have higher values of viscosity factor The vibration amplitude of a beam with larger values of viscosity factor is smaller than those with lower values Also the settle time of systems with higher values of viscosity factor is less than the others Increasing the rotary inertia factor leads to larger values of both time period and amplitude of oscillations at each moment Increasing the flexural rigidity factor reduces both the amplitude and time period of vibration response In primary and superharmonic resonances with increasing the viscoelastic factor and decreasing the amplitude of excitation the amplitude of the steady state response has been decreased It has been shown that instability and bifurcation point is in the type of saddle point In subharmonic and primary resonance cases jump phenomenon can be observed Keyword Axially moving Rayleigh b

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بررسي ارتعاشات غير خطي و پديده دوشاخه اي شدن تير ويسكوالاستيك منحرك در راستاي محور

تير ريلي , مقياس زماني چندگانه مستقيم , نيوتن - رافسون , تشديد اصلي , تشديد زير هارمونيك , تشديد بالاي هارمونيك , پايداري , پرش