Mechanical Engineering / Makina Mühendisliği

Permanent URI for this collectionhttps://hdl.handle.net/11147/4129

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  • Other
    Citation - WoS: 4
    Citation - Scopus: 4
    Exact Solutions for the Longitudinal Vibration of Non-Uniform Rods [j. Sound Vib. 207 (1997) 721-729]
    (Academic Press Inc., 2010) Yardımoğlu, Bülent
    The aims of this communication are to correct the frequency equation for a free–free rod with area variation A(x)=A0 s in2(ax+b) in a published article [1] and present the corrected non-dimensional natural frequencies.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 33
    Coupled Out of Plane Vibrations of Spiral Beams for Micro-Scale Applications
    (Academic Press Inc., 2010) Karami, M. A.; Yardımoğlu, Bülent; Inman, Daniel J.
    An analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.
  • Article
    Citation - WoS: 39
    Citation - Scopus: 46
    Finite Element Model for Vibration Analysis of Pre-Twisted Timoshenko Beam
    (Academic Press Inc., 2004) Yardımoğlu, Bülent; Yıldırım, Tolga
    A new linearly pre-twisted Timoshenko beam finite element, which has two nodes and four-degrees-of-freedom per node, is developed and subsequently used for coupled bending-bending vibration analysis of pre-twisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pre-twisted beams whose flexural displacements are coupled in two planes. This approach helps to reduce the number of nodal variables. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pre-twisted Timoshenko beams are obtained and compared with previously published theoretical and experimental results to confirm the accuracy and efficiency of the present model. Excellent agreement is found with the previous studies. Also, the new pre-twisted Timoshenko beam element has good convergence characteristics.