Abstract
The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilibrium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.
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References
Alwis, W.A.M., Wang, C.M., 1996. Wagner term in flexural-torsional buckling of thin-walled open profile columns. Engineering Structures, 18(2):125–132. [doi:10.1016/0141-0296(95)00112-3]
Friberg, P.O., 1985. Beam element matrices derived from Vlasov’s theory of open thin-walled elastic beams. International Journal for Numerical Methods in Engineering, 21(7):1205–1228. [doi:10.1002/nme.1620210704]
Gao, X.N., Wu, L.L., Zhu, H.M., 2005. Interactive local buckling analysis of corrugated plate assemblies of channel sections under uniform compression. Journal of Building Structures, 26(1):39–44 (in Chinese).
Kubiak, T., 2005. Dynamic buckling of thin-walled composite plates with varying widthwise material properties. International Journal of Solids and Structures, 42(20):5555–5567. [doi:10.1016/j.ijsolstr.2005.02.043]
Lee, U., Shin, J., 2002. A frequency-domain method of structural damage identification formulated from the dynamic stiffness equation of motion. Journal of Sound and Vibration, 257(4):615–634. [doi:10.1006/jsvi.2002.5058]
Leung, A.Y.T., 1993a. Dynamic Stiffness and Substructures. Springer-Verlag, London, UK, p.189–240.
Leung, A.Y.T., 1993b. Non-conservative dynamic stiffness analysis of thin-walled structures. Computers & Structures, 48(4):703–709. [doi:10.1016/0045-7949(93)90263-D]
Leung, A.Y.T., Zhou, W.E., Lim, C.W., Yuen, R.K.K., Lee, U., 2001a. Dynamic stiffness for piecewise non-uniform Timoshenko column by power series—part I: Conservative axial force. International Journal of Numerical Methods in Engineering, 51(5):505–529. [doi:10.1002/nme.159.abs]
Leung, A.Y.T., Zhou, W.E., Lim, C.W., Yuen, R.K.K., Lee, U., 2001b. Dynamic stiffness for piecewise non-uniform Timoshenko column by power series—part II: Follower force. International Journal for Numerical Methods in Engineering, 51(5):531–552. [doi:10.1002/nme.153.abs]
Libai, A., Simmonds, J.G., 1998. The Nonlinear Theory of Elastic Shells, 2nd Ed. Cambridge University Press, Cambridge, p.21–50.
Saade, K., Espion, B., Warzee, G., 2004. Non-uniform torsional behaviour and stability of thin-walled elastic beams with arbitrary cross sections. Thin-walled Structures, 42(6):857–881. [doi:10.1016/j.tws.2003.12.003]
Yang, Y.B., Yau, J.D., Wu, Y.S., 2004. Vehicle-bridge Interaction Dynamics. World Scientific, Singapore, p.153–198.
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Project (No. 9040831) supported by the Hong Kong Research Grant Council, China
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Zhu, B., Leung, A.Y.T. Dynamic stiffness for thin-walled structures by power series. J. Zhejiang Univ. - Sci. A 7, 1351–1357 (2006). https://doi.org/10.1631/jzus.2006.A1351
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DOI: https://doi.org/10.1631/jzus.2006.A1351