فهرست مطالب سعید باب

Nowadays, the use of wind as one of the main sources of low carbon and renewable energy is expanding rapidly all around the world. Recently, with the development of wind farms and the consequent increase in the size of wind turbines, their maintenance has become more difficult. Therefore, researchers have deeply focused on the analysis and the control of their vibration. In this study, a wind turbine blade with a type of nonlinear absorber, called highly efficient nonlinear energy sink is analyzed, and the interaction between the heavy and long blade and the nonlinear energy sink (NES), under the influence of gravity in the vertical plane and wind force varying periodically due to height dependence is examined. For this purpose, the equations of motion for the blade connected to the NES are extracted using the energy method and solved numerically. Finally, the sensitivity of the parameters affecting the performance of the NES is analyzed and the performance of the system under rotation of the standalone blade and also the rotation of the blade in the presence of the optimal NES is studied.

Recently, modern turbines are designed close to their critical operating points with lower stability margin. Therefore, accurate dynamic analysis and using advanced vibration control systems are required. In this paper, the application of nonlinear energy sinks (NESs) for indirect vibration reduction of the blades in a flexible shaft-disk-blades system of a real steam turbine is conducted. 37 packets of seven-connected blades are mounted on the perimeter of the disk. The cyclic finite element analysis is employed to obtain mode shapes and frequency diagram. For the second combined mode of system, which is a combination of the second bending mode of shaft and the third bending mode of disk-blades, a two degrees of freedom (2DOFs) reduced order model (ROM) is identified for each sector. The cyclic symmetry of ROM reduces the size of the studied model to 2 DOFs. NESs with a small mass, an essential nonlinear stiffness and a linear damping are installed on the ROM in the antinode position of desired mode. The Runge-Kutta method is used to solve the nonlinear equations numerically. Optimum stiffness and damping of the NESs are determined to minimize the vibration amplitude of the blades.The results show the occurrence of strongly modulated response around the resonance, and hence, the desired vibration reduction of the blades is take placed. If the NESs have large nonlinear stiffness or low damping, a saddle-node bifurcation and a large island form near the resonance, and the blades could experience large amplitude periodic motion in the negative detuning frequencies.

In this paper, the application of passive vibrational linear absorber on the indirect reduction of blade vibrations using its mounted on the disk-blade system is studied. The absorber receives the vibration energy of blade through a structural coupling of the disk with blade and losses it by its linear damping. Due to cyclic symmetry, the analysis of the bladed disk is reduced to the number of DOFs in a single sector. A cyclic transformation from physical to modal coordinates is used to perform this reduction. Natural frequencies and forced responses of the system are obtained by solving the characteristic and algebraic equations, respectively. The case study of a steam turbine includes 259 blades in 37 packets of 7 connected blades attached to the perimeter of the disk. Cyclic symmetric finite element analysis at 3000rpm is used to extract the natural modes and frequency diagram of the system. A two DOFs reduced-order model is identified for modeling the frequency-veering region. This region has been formed between the first and second families of natural modes and there is a strong coupling between them in this region. In addition, this region is close to the system excitation line and the possibility of resonance exists. Therefore, some linear energy absorbers are mounted on the disk for the indirect vibration reduction of blades. The initial optimal parameters were determined for the first and second modes using Den Hartog relations. These parameters reduced the system vibrations and they were used in subsequent optimization. The optimization has resulted in the improvement of absorber performance exclusively around the second mode, in compare with the tuned system by Den Hartog relations.

In this paper the dynamic behavior of a rotating system which includes rotor (shaft), ball bearing and disk in stationary condition and different speeds is investigated. There are nonlinear characteristics in these systems which cause the linear modeling is not sufficiently accurate. So, in this paper the nonlinear dynamic equations of the system are derived and solved. To derive the equations of the system, Hamiltonian method is used, and complex coordinate transform is used to reduce the number of equations. After solving the equations, to investigate the vibrational properties of the system, time response diagram, dynamic orbit, frequency response, and mode shape of the rotor is plotted. To validate the analytical results, finite element method by ANSYS (workbench) software is used.There is a good conformity betweenthe analytical results and finite element results in resonance frequencies of the system in the first three modes which indicates the sufficient accuracy in nonlinear modeling. It can be concluded from nonlinear modeling that the decay rate is negative for the all modes which is indicates the stability of the all modes. Also, the maximum vibration amplitude in the bearing and rotor occurs in third and second modes respectively. Unbalance phase difference of 90 degrees in two discs causes the excitation of all three frequency modes, whereas by unbalance phase difference of 0 or 180 degrees in two discs,only the odd modes (first and third) and the even modes (second) is excited respectively.