Kerim Can ÇELEBİ, Naki TÜTÜNCÜ, İBRAHİM KELEŞ

Değişken kesitli elastik çubukların dinamik yükler altındaki davranışının Laplace transform metodu ile analizi

Sürekli sistem olarak modellenen eksenel yüklenmiş değişken kesitli bir çubuğun elastik davranış problemi analiz edilmiştir. Malzeme özellikleri olarak çelik özellikleri seçilmiştir. Analizde Laplace dönüşüm metodu kullanılmış ve zaman uzayındaki çözüm nümerik Laplace ters dönüşüm yöntemi kullanılarak bulunmuştur. Sonuçlar, her bir alan tipi ve yükleme tipi için oluşturulan grafiklerle sunulmuştur.

Analysis of behaviour of an elastic bar with varying cross-section under dynamic loads with Laplace transform method

The axial vibration problem formulation and solution of a bar of varying cross- section modeled as a continuous system were analyzed. The material properties are those of structural steel. Solutions are obtained using Laplace transform method. The solution in the time domain was obtained by an appropriate numerical inverse Laplace transformation method. The results are presented in the form of graphs for each area and load type.

___

1. Çelebi,K., “Analysis of On-Dimensional Response of an Elastic Body Under Dynamic Loads”, Cukurova University Institute of Natural and Applied Science, MSc Thesis, 2004.
2. Beskos,D.E. and Narayanan,G.V., “Dynamic Response of Frameworks by Numerical Laplace Transform”, Computer Methods In Applied Mechanics and Engineering, 37: 289-307,1983.
3. Durbin,F., “Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate’s Method”, Commissariat a l’Energie Atomique Centre U-Service Electronique, 17: 371-376. 1974.
4. Abrate,S., “Vibration of Non-Uniform Rods and Beams”, Journal of Sound and Vibration, 185(4): 703-716, 1995.
5. Li,Q.S., Li,G.Q. and Liu,D.K., “Exact Solutions for Longitudinal Vibration of Rods Coupled by Translational Springs”, International Journal of Mechanical Sciences, 42: 1135-1152, 1999.
6. Kumar,B.M. and Sujith,R.I., “Exact Solutions for the Longitudinal Vibration of Non-Uniform Rods”, Journal of Sound and Vibration, 207(5), 721-729, 1997.
7. Narayanan,G.V., “Use of Dynamic Influence Coefficients in Forced Vibration Problems with the Aid of Fast Fourier Transform”, Computers and Structures, 9,145-150, 1977.
8. Temel,B., Yüksek Lisans Tezi, Çukurova Üniversitesi, İnşaat Mühendisliği Bölümü, Adana, 219 s., 1995.