Öz
Bu çalışmada, elastik kütle-yay sarkaç salınımları incelenmiştir. Sistemin lineer olmayan diferansiyel denklemlerini çözmek için Dymola, SimulationX gibi Modelica dili tabanlı Simülasyon Tekniği kullanılmıştır. Sistemdeki yayın direngenliği lineer ve kütlesi ihmal edilmiştir. Bu şartlar altındaki sarkacın kinematik davranışı incelenmiştir. Sistemi ifade eden genel denklem iki tane lineer olmayan ve birbirini etkileyen diferansiyel denklemden oluşmaktadır. Bu denklemler Simülasyon Tekniği ile çözülmüştür. Elde edilen sonuçlar önceki çalışmalarla kıyaslanmış ve uyumlu olduğu görülmüştür.
Anahtar Kelimeler
Elastik sarkaç Lineer olmayan salınım Simülasyon Tekniği Modelica Dymola.
Kaynakça
- Chang, C. L. and Lee, Z. Y. 2004. Applying the double side method to solution nonlinear pendulum problem, Appl. Math.Comput. 149, 613-624.
- Fung, T. C. 2001. Solving initial value problems by differential quadrature method. part 2: second- and higher-order equations, Int. J. Numer. Meth. Eng. 50, 1429-1454.
- Georgiou, I. T. 1999. On the global geometric structure of the dynamics of the elastic pendulum, Nonlinear Dynam. 18, 51-68.
- Girgin, Z. 2008. Combining differential quadrature method with simulation technique to solve non- linear differential equations, Int. J. Numer. Meth. Eng. 75 (6), 722-734.
- He, J. H. 1999. Variational iteration method – a kind of nonlinear analytical technique: some examples, Int. J. Nonlin. Mech., 34 (4), 699-708.
- He, J. H. 2003. Homopoty perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135 (1), 73-79.
- Liu, G. R. and Wu, T. Y. 2000. Numerical solution for differential equations of duffing-type non- linearity
- quadrature rule, J. Sound. Vib. 237 (5), 805-817. generalized
- differential Lynch, P. 2002. Resonant motions of the three- dimensional elastic pendulum, Int. J. Nonlinear Mech. 37, 345-367.
- Lynch, P. and Houghton, C. 2004. Pulsation and precession of the resonant swinging spring, Physica D, 190, 38-62.
- Nayfeh, A. H. 1987. Nonlinear oscillations 720s. A Wiley-Interscience Publication.
- Vetyukov, Y., Gerstmayr, H. and Irschik, H. 2004. The Comperative Analysis of the fully nonlinear, the linear elastic and the consistently linearized equations of motion of the 2d elastic pendulum, Comput. Struct. 82, 863-870.
Öz
In this study, elastic spring-mass pendulum oscillations are investigated. In order to solve a nonlinear differential equation system, Simulation Technique based on Modelica Language such as Dymola, SimulationX etc., is used. It's assumed that the spring coefficient in this system is linear and spring mass is neglected. Under these conditions, kinematic behavior of the pendulum was investigated. The governing equation of the system possessing two nonlinear differential equations which interacts each other are solved simultaneously. The obtained results are compared with previous works and seemed good agreements with others.
Anahtar Kelimeler
Elastic pendulum Nonlinear oscillation Simulation technique Modelica Dymola.
Kaynakça
- Chang, C. L. and Lee, Z. Y. 2004. Applying the double side method to solution nonlinear pendulum problem, Appl. Math.Comput. 149, 613-624.
- Fung, T. C. 2001. Solving initial value problems by differential quadrature method. part 2: second- and higher-order equations, Int. J. Numer. Meth. Eng. 50, 1429-1454.
- Georgiou, I. T. 1999. On the global geometric structure of the dynamics of the elastic pendulum, Nonlinear Dynam. 18, 51-68.
- Girgin, Z. 2008. Combining differential quadrature method with simulation technique to solve non- linear differential equations, Int. J. Numer. Meth. Eng. 75 (6), 722-734.
- He, J. H. 1999. Variational iteration method – a kind of nonlinear analytical technique: some examples, Int. J. Nonlin. Mech., 34 (4), 699-708.
- He, J. H. 2003. Homopoty perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135 (1), 73-79.
- Liu, G. R. and Wu, T. Y. 2000. Numerical solution for differential equations of duffing-type non- linearity
- quadrature rule, J. Sound. Vib. 237 (5), 805-817. generalized
- differential Lynch, P. 2002. Resonant motions of the three- dimensional elastic pendulum, Int. J. Nonlinear Mech. 37, 345-367.
- Lynch, P. and Houghton, C. 2004. Pulsation and precession of the resonant swinging spring, Physica D, 190, 38-62.
- Nayfeh, A. H. 1987. Nonlinear oscillations 720s. A Wiley-Interscience Publication.
- Vetyukov, Y., Gerstmayr, H. and Irschik, H. 2004. The Comperative Analysis of the fully nonlinear, the linear elastic and the consistently linearized equations of motion of the 2d elastic pendulum, Comput. Struct. 82, 863-870.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makale |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Ocak 2009 |
| Yayımlandığı Sayı | Yıl 2009 Cilt: 15 Sayı: 1 |
