چكيده به لاتين
This thesis is devoted to studying mode localization phenomenon in nonlinear structures. The main objective of this investigation is to observe mode localization phenomenon experimentally in a symmetric structure with geometric nonlinearity. For this aim, a rectangular plate which two beams are cut on it, has been designed and prepared for experiments. This structure provides good conditions to have two coupled oscillators with low coupling damping. The modal analysis of the finite element model has been performed in ANSYS 18.0.
By increasing the level of excitation which leads to the large amplitude of vibration, the nonlinear behavior of structure can be observed. The nonlinear behavior generates many phenomena that has no counterparts in the linear theory. Mode localization is one of these phenomena which can be generated in nonlinear structures. Mode localization can be defined as confinement energy on a small portion of the system. It means, in two oscillators system, one of the oscillators vibrates with large amplitude while the other one is almost motionless.
To reduce the order of model STEP (Stiffness Evaluation Procedure) method has been applied and nonlinear coefficients of the Duffing equation have been extracted to use them in the next step of the problem. To anticipate bifurcation points and mode localization, numerical methods have been used. In this thesis, nonlinear equations have been solved theoretically by using multiple scales method and the procedures of solving with this method are explained in detail. Also, numerical results have been extracted by using MANLAB, which is a continuation tool to simplify bifurcation analysis and study nonlinear dynamical structures. This method is based on the Harmonic Balance Method.
To validate numerical results and observe mode localization phenomenon an experimental work have been carried out. It is shown that by this structure and devices, it is not possible to reach bifurcation points, consequently mode localization could not be observed.
Keywords: Nonlinear vibration, Geometric nonlinearities, Continuation method, Model order reduction, Mode localization.
