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    Öğe
    Effect of magneto-thermal loads on the rotational instability of heterogeneous rotors
    (Amer Inst Aeronautics Astronautics, 2019) Yıldırım, Sefa; Tütüncü, Naki
    Magnetic field and thermal loads are present in the operating environment of jet engine parts such as turbine rotors. Therefore, their influence on the burst velocity of rotors is worthy of investigation. The present paper addresses the analysis of rotational elastic instability in heterogeneous disks having variable thickness under magnetic field and thermal loading. Inclusion of the radial displacement in the centrifugal force indicates rotational instability at certain angular velocities. Closed-form expressions for the displacement and stresses are not possible due to variable material properties, thickness profile, thermal expansion, and conduction coefficients of the disk. The Complementary Functions Method is adopted as a numerical solution scheme. The results are obtained in terms of nondimensional parameters to achieve high accuracy with few collocation points. The burst velocities under influences of magnetic field and thermal loads are calculated. Redistributed hoop stresses are also plotted against angular velocity for different magnetic intensity and temperature changes. It is concluded that magnetic field has a stabilizing effect on the rotating heterogeneous disk and the influence of thermal load is negligible in the rotational stability analysis.
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    Öğe
    Numerical methods in calculating eigenvalues: Case studies in stability of euler columns
    (Alanya Alaaddin Keykubat Üniversitesi, 2019) Jamil, Hammad; Tütüncü, Naki
    A comparative analysis of well renowned “Shooting Method” with another numerical method “Complementary Functions Method” (CFM) is presented for calculating eigenvalue (?). Contrary to the shooting method hit and trial approach, CFM exploits the properties of linear ordinary differential equation (LODE). In the case of linear eigenvalue Boundary value Problem (BVP), CFM generates an algebraic equation system with one unknown “?” and, alone root finding method is sufficient to give required eigenvalue. However, the Shooting Method create a system of algebraic equations containing two unknowns “?” and “missing initial conditions”, that demands an additional numerical technique along with root finding method. These radical differences between two approaches, sets the basis for this comparative investigation. As a case study in Linear Elastic Stability, different cases of Euler columns are investigated by finding eigenvalues for each case numerically, under both methods. Comparison is performed on the basis of results accuracy and cost effectiveness for both numerical techniques while solving linear stability problems.