Effect of spring mid-support condition on the vibrations of the axially moving string

In this study, the axially moving string with spring-loaded middle support is discussed. The supports assumed as simple support on the string both ends. The intermediate support shows the characteristics of the spring. The string velocity is accepted as harmonically varying around a mean value. The Hamiltonian principle is used to find the equations of motion. The equations of motion become nonlinear, considering the nonlinear effects caused by string extensions. The equations of motion and boundary conditions are become dimensionless by nondimensionalization. Approximate solutions were found by using multiple time scales which is one of the perturbation methods. By solving the linear problem that is obtained by the first terms of the perturbation series, the exact natural frequencies were calculated for the different locations of the mid-support, various spring coefficients, and various axial velocity values. The second-order nonlinear terms reveal the correction terms for the linear problem. Stability analysis is carried out for cases where the velocity change frequency is away from zero and two times the natural frequency. Stability boundaries are determined for the principal parametric resonance case.

Keywords:

Axially moving string, Perturbation method, Spring supported string Vibration analysis,

PDF

___

1. Thurman, A. L., Mote, C.D., Free, Periodic, Nonlinear Oscillation of an Axially Moving Strip. Journal of Applied Mechanics, 1969. 36(1): p. 83-91.
2. Ulsoy, A.G., Mote, C.D. Jr., and Syzmani, R., Principal developments in band saw vibration and stability research. Holz als Roh- und Werkstoff, 1978. 36(7): p. 273-280.
3. Wickert, J.A., Mote, C.D. Jr., Current research on the vibration and stability of axially moving materials. Shock and Vibration Digest, 1988. 20(5): p. 3-13.
4. Wickert, J.A., Response solutions for the vibration of a traveling string on an elastic foundation. Journal of Vibration and Acoustics, 1994. 116(1): p. 137–139.
5. Nayfeh, A.H., Nayfeh, J.F., Mook, D.T., On methods for continuous systems with quadratic and cubic nonlinearities. Nonlinear Dynamics, 1992. 3: p. 145-162.
6. Pellicano, F., Zirilli, F., Boundary layers and non-linear vibrations in an axially moving beam. International Journal of Non-Linear Mechanics, 1998. 33(4): p. 691-711.
7. Kural, S., Özkaya, E., Vibrations of an axially accelerating, multiple supported flexible beam. Structural Engineering and Mechanics, 2012. 44(4): p. 521-538.
8. Yurddaş, A., Özkaya, E., Boyacı, H., Nonlinear vibrations and stability analysis of axially moving strings having nonideal mid-support conditions. Journal of Vibration and Control, 2012. 20(4): p. 518–534.
9. Pellicano F., On the dynamic properties of axially moving system. Journal of Sound and Vibration, 2005. 281(3-5): p. 593–609.
10. Bağdatli, S.M., Özkaya, E., Öz, H.R., Dynamics of Axially Accelerating Beams with an Intermediate Support. Journal of Vibration and Acoustics, 2011. 133(3): 031013,10 pages.
11. Ghayesh, M. H., Amabili, M. Païdoussis, M. P., Nonlinear vibrations and stability of an axially moving beam with an intermediate spring support: two-dimensional analysis. Nonlinear Dynamics, 2012. 70(1): p. 335-354.
12. Nguyen, Q. C., Hong, K.S., Simultaneous control of longitudinal and transverse vibrations of an axially moving string with velocity tracking. Journal of Sound and Vibration, 2012. 331(13): p. 3006-3019.
13. He, W., Ge, S. S., Huang, D., Modeling and vibration control for a nonlinear moving string with output constraint. IEEE/ASME Transactions on Mechatronics, 2015. 20(4): p. 1886-1897.
14. Xia, C., Wu, Y., Lu, Q., Experimental study of the nonlinear characteristics of an axially moving string. Journal of Vibration and Control, 2015. 21(16): p. 518–534.
15. Sun, W., Sun, Y., Yu, Y., Zheng, S., Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method. Structural Engineering and Mechanics, 2016. 59(1): p. 1-14.
16. He, W., Nie, S., Meng, T., Liu, Y.-J., Modeling and vibration control for a moving beam with application in a drilling riser. IEEE Transactions on Control Systems Technology, 2017. 25(3): p. 1036-1043.
17. Vetyukov, Y., Non-material finite element modelling of large vibrations of axially moving strings and beams. Journal of Sound and Vibration, 2018. 414(3): p. 299–317.
18. Chen, E. , Li, M., Ferguson, N., Lu,Y., An adaptive higher order finite element model and modal energy for the vibration of a traveling string. Journal of Vibration and Control, 2018. 25(5): p. 996–1007.
19. Zhao, Z., Ma, Y., Liu, G., Zhu, D., Wen, G., Vibration Control of an Axially Moving System with Restricted Input. Complexity, 2019. 2019: Article ID 2386435, 10 pages.
20. Zhang, X., Pipeleers, G., Hengster-Movrić, K., Faria, C., Vibration reduction for structures: distributed schemes over directed graphs. Journal of Vibration and Control, 2019. 25(14): p. 2025–2042.
21. Yılmaz, Ö , Aksoy, M , Kesi̇lmi̇ş, Z ., Misalignment fault detection by wavelet analysis of vibration signals. International Advanced Researches and Engineering Journal, 2019. 3(3): p. 156-163.

International Advanced Researches and Engineering Journal-Cover

Yayın Aralığı: Yılda 3 Sayı
Başlangıç: 2017
Yayıncı: Dr. Ceyhun YILMAZ

Arşiv