Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Subject: search.filters.subject.Equations of motion

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  • Article
    Citation - WoS: 15
    Citation - Scopus: 19
    Exact Longitudinal Vibration Characteristics of Rods With Variable Cross-Sections
    (Hindawi Publishing Corporation, 2011) Yardımoğlu, Bülent; Aydın, Levent
    Longitudinal natural vibration frequencies of rods (or bars) with variable cross-sections are obtained from the exact solutions of differential equation of motion based on transformation method. For the rods having cross-section variations as power of the sinusoidal functions of ax+b, the differential equation is reduced to associated Legendre equation by using the appropriate transformations. Frequency equations of rods with certain cross-section area variations are found from the general solution of this equation for different boundary conditions. The present solutions are benchmarked by the solutions available in the literature for the special case of present cross-sectional variations. Moreover, the effects of cross-sectional area variations of rods on natural characteristics are studied with numerical examples.
  • 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.