Vibrations of fluid conveying micro beams under non-ideal boundary conditions

In this thesis, vibration behaviors of fluid conveying micro beams under non-ideal boundary conditions are investigated. Micro beam which is under the effect of the moving fluid is modeled by considering the micro size effects and nonlinear equations of motion are obtained by using Hamilton's Principle. Micro beam is assumed to be under the effect of the electrical field force and the velocity of inner fluid is assumed to be harmonically varying around a constant value. Governing equations of motion are non-dimensionalized in order to obtain a general solution which is independent of the material and geometric properties of the system. Non-ideal boundary conditions are expressed as a linear combination of ideal clamped and ideal simply supported boundary conditions. The physical condition of non-ideal boundary condition is determined by an additional weighting factor to the aforementioned expression. Approximate solutions of the system are found by applying multiple time scale method, which is a perturbation technique, to the obtained equation of motion and the boundary conditions. The system parameters like micro size effect, damping parameter, micro beam fullness ratio are commented in terms of the effects of non-ideal boundary conditions. The comparisons of the solutions with the ones which are obtained by the assumption of ideal boundary conditions are given. The cases of fundamental parametric resonance; where the changing frequency of fluid velocity is close to two times of the natural frequency, primary resonance; where the changing frequency of electrical field force is close to natural frequency and the special resonance; which includes the first two cases are investigated and stability analysis for the solutions are performed.