Dynamical Analysis of the Multispan Beams with Method of Multiple Scales

Abstract

Multi-span beams are statically indeterminate structures in general. They have many applications in civil engineering, mechanism, navigation engineering and so on. For example, multi-span bridges have been widely used in highway and railway. It is of great importance to study the dynamic characteristic of the multi-span beams for engineering design and scientific research. Many engineers and scientists have contributed to the solution of the problem with their innovations, and still the subject draws considerable attention from researchers by now. In this study, we investigate primary resonance case of multi-span beam subject to axial load. Firstly, the mathematical model of the problem is derived by using extended Hamilton principle. This model has geometric nonlinearity. Here, two system of partial differential equations are obtained for axial direction and transverse direction. The numbers of equations and boundary conditions depends on span number. After coupling equations in transverse and axial directions, the system of nonlinear integro-differential equations are obtained and solved using the method of multiple time scales.

Keywords

• Method of multiple scales,nonlinear vibration,multi-span beam,primary resonance

Dynamical Analysis of the Multispan Beams with Method of Multiple Scales

Abstract

Multi-span beams are statically indeterminate structures in general. They have many applications in civil engineering, mechanism, navigation engineering and so on. For example, multi-span bridges have been widely used in highway and railway. It is of great importance to study the dynamic characteristic of the multi-span beams for engineering design and scientific research. Many engineers and scientists have contributed to the solution of the problem with their innovations, and still the subject draws considerable attention from researchers by now. In this study, we investigate primary resonance case of multi-span beam subject to axial load. Firstly, the mathematical model of the problem is derived by using extended Hamilton principle. This model has geometric nonlinearity. Here, two system of partial differential equations are obtained for axial direction and transverse direction. The numbers of equations and boundary conditions depends on span number. After coupling equations in transverse and axial directions, the system of nonlinear integrodifferential equations are obtained and solved using the method of multiple time scales.

Keywords

• Method of multiple scales,nonlinear vibration,multi-span beam,primary resonance

References

1. Henchi K., Fafard M., Dhatt G., Talbot M. 1997. Dynamic behaviour of multi-span beams under moving loads 199, 33-50.
2. Bağdatlı S.M., Özkaya E., Öz H.R. 2013. Dynamics of axially accelerating beams with multiple supports 74, 237–255.
3. Kesimli A., Özkaya E., Bağdatlı S. M. 2015. Nonlinear vibrations of spring-supported axially moving string 81, 1523–1534.
4. Bao-hui L., Hang-shan G., Hong-bo Z., Yong-shou L., Zhu-feng Y., 2011. Free vibration analysis of multi-span pipe conveying fluid with dynamic stiffness method, 241, 666–671.
5. Dönmez Demir D., Sınır B.G., Usta L. 2016. Determining Critical Load in the Multi-span Beams with the Nonlinear Model, ICNPAA2016 World Congress11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, La Rochelle, France.