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In this study, a novel model is developed to investigate the angular acceleration of the nonlinear misaligned rotor passing through the critical speeds under non-stationary operating conditions. The concerned rotor is modeled elastic with the effects of nonlinear inertia terms and flexible bearing. Nonlinear equations of motion are derived using the Lagrange method and solved with the finite element method. Effects of parameters such as shaft eccentricity, damping, and stiffness of the supports on the increase in the rotor angular speed passing through the critical speed are considered. The obtained results indicate that a small amount of eccentricity prevents exceeding the elastic critical speed of the rotor. According to the results, if the support parameters are not selected properly, the rotor will not even be able to pass its rigid critical speed. [ABSTRACT FROM AUTHOR]

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed. [ABSTRACT FROM AUTHOR]

This study considers the aeroelastic instability of a partially treated magneto-rheological fluid sandwich panel in supersonic airflow. The linear first-order piston theory is used for modeling the aerodynamic pressure. Using classical Hamilton's principle along with the finite element method, the equations of motion are derived. The critical value of the non-dimensional aerodynamic pressure is obtained by traditional p-method scheme. The validity of the finite element formulation is examined through comparison with those obtained from the assumed mode formulation and the available results in the literature. Various parametric studies including the effects of applied magnetic field, core and constraining layer thicknesses are examined for several configurations of the core at simply-supported and clamped–clamped boundary conditions. The results show that the critical non-dimensional aerodynamic pressure of the sandwich panel is influenced not only by the magnetic field strength, core and constraining layer thicknesses but also strongly by the configuration of the core. [ABSTRACT FROM AUTHOR]