KERİMCAN ÇELEBİ, DURMUŞ YARIMPABUÇ, MEHMET EKER

Tamamlayıcı Fonksiyonlar Yöntemi ile Heterojen Bir Çubuğun Zorlanmış Titreşim Analizi

Sürekli sistem olarak modellenen eksenel yüklenmiş heterojen bir çubuğun elastik davranış problemi analiz edilmiştir. Bu problemi modelleyen diferansiyel denklemlere Laplace dönüşümü uygulanarak zamandan bağımsız sınır değer problemi eksenel koordinatlarda elde edilmiş daha sonra bu problem tamamlayıcı fonksiyonlar metodu (TFM) tarafından çözülmüştür. Sayısal olarak çözülen denklemler Durbin'in sayısal ters dönüşümünü yardımıyla zaman uzayına dönüştürülmüştür. Her bir yükleme tipi ve inhomojenlik parametresi için elde edilen sayısal sonuçlar, analitik sonuçlar ve ANSYS sonuçları ile karşılaştırılmıştır. Bu birleşik yöntem, iyi yapılandırılmış, basit ve etkili bir yöntemdir

Forced Vibration Analysis of A Heterogeneous Rod by Complementary Functions Method

The axial vibration problem formulation and solution of a heterogeneous rod modelled as a continuous system were analyzed. By applying Laplace transformation to the differential equations that model to this problem, time independent boundary value problems were obtained in the axial coordinates, then this problem is solved by the complementary functions method. The equations solved numerically is converted into time space with the help of Durbin's numerical inverse transformation. The numerical results that obtained for each load type and inhomogeneity parameter were compared with analytical and ANSYS results in the literature. This unified method is well-structured, simple and efficient

___

Raj, A., Sujith, R.I., 2005. Closed-form Solutions for the Free Longitudinal Vibration of Inhomogeneous Rods, J. Sound. Vib. 283, 1015-1030.

Nachum, S., Altus, E., 2007. Natural Frequencies and Mode Shapes of Deterministic and Tochastic Non-homogeneous Rods and Beams, J. Sound. Vib., 302, 903-924.

Horgan, C.O., Chan, A.M., 1999. Vibration of Inhomogeneous Strings, Rods and Membranes, J. Sound. Vib. 225, 503-513.

Abrate , S., 1995. Vibration of Non-uniform Rods and Beams, Journal of Sound and Vibration. 185, 703-716.

Kumar, B.M., Sujith, R.I., 1997. Exact Solutions for the Longitudinal Vibration of Non-uniform Rods, Journal of Sound and Vibration, 207,5, 721-729.

Li, Q.S., 2000. Exact Solutions for Free Longitudinal Vibration of Non-uniform Rods, Journal of Sound and Vibration, 234, 1, 1-19.

Li, Q.S., 2000. Exact Solutions for free Longitudinal Vibration of Bars with Non- uniform Cross-section, Journal of Applied Mechanics and Engineering, 5, 3, 521-541.

Li, Q.S., 2000. Exact Solutions for Longitudinal Vibration of Multi-step Bars with Varying Cross-section, Journal of Vibration and Acoustics, 122, 183-187.

Celebi, K., Keles, I., Tutuncu, N., 2011. Exact Solutions for Forced Vibration of Non-uniform Rods by Laplace Transformation, Gazi University Journal of Science, 24,2, 347-353.

Celebi, K., Keles, I., Tutuncu, N., 2012. Closed-form Solutions for Forced Vibration Analysis of Inhomogeneous Rod, J. Fac. Eng. Archit. Gaz., 27, 4, 753-763.

Shokrollahi, M., Nejad, Numerical Analysis of Free Longitudinal Vibration of Nonuniform Rods: Discrete Singular Convolution Approach, Journal of Engineering Mechanics, 140, 8. 2014.

Aktas, Z., 1972. Numerical Solutions of Two- point Boundary Value Problems, METU, Department of Computer Eng., Ankara, Turkey.

Roberts, S.M., Shipman, J.S., 1979. Fundamental Matrix and Two-point Boundary- Value Problems, Journal of Optimization Theory and Application, 28, 1, 77-78.

Agarwal,R.P., 1982. On the Method of Complementary Functions for Nonlinear Boundary-value Problems, Journal of Optimization Theory and Applications, 36, 1, 139-144.

Yıldırım,V., 1997. Free Vibration Analysis of Non-cylindrical Coil Springs by Combined use of the Transfer Matrix and the Complementary Functions Methods, Communications in Numerical Methods in Engineering, 13, 487-494.

Calim,F.F., 2009. Free and Forced Vibration of Non-uniform Composite Beams, Composite Structures,88, 413-423.

Tütüncü,N., Temel B., 2009. A Novel Approach to Stress Analysis of Pressurized FGM Cylinders, Disks and Spheres, Composite Structure, 91, 385-390.

Durbin,F., 1974. Numerical Inversion of Laplace Transforms: an Efficient Improvement to Dubner and Abate's Method, The Computer Journal, 17, 371-376.