Abstract
The free vibration and transient wave in a prestressed Rayleigh-Timoshenko beam subject to arbitrary transverse forces are analyzed by the newly developed method of reverberation-ray matrix (MRRM). The effects of shear deformation and rotational inertia are taken into consideration. With a Fourier transform technique, the general wave solutions with two sets of unknown amplitude coefficients are obtained in the transformed domain for an unbonded prestressed beam under the action of arbitrary external excitations. From the coupling at joints and the compatibility of displacements in each member, the free and forced vibration responses of a beam with various boundary conditions are finally evaluated through certain numerical algorithms. Results are presented for a simply-supported beam subject to either a point fixed load or moving load. Good agreement with the finite element method (FEM) is obtained. The present work is instructive for high-speed railway bridge design and structural health monitoring.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Auciello, N.M., Ercolano, A., 2004. A general solution for dynamic response of axially loaded non-uniform Timoshenko beams. International Journal of Solids and Structures, 41(18-19):4861–4874. [doi:10.1016/j.ijsolstr.2004.04.036]
Bokaian, A., 1988. Natural frequencies of beams under compressive axial loads. Journal of Sound and Vibration, 126(1):49–65. [doi:10.1016/0022-460X(88)90397-5]
Bokaian, A., 1990. Natural frequencies of beams under tensile axial loads. Journal of Sound and Vibration, 142(3): 481–498. [doi:10.1016/0022-460X(90)90663-K]
Chen, J.F., Pao, Y.H., 2003. Effects of causality and joint conditions on method of reverberation-ray matrix. AIAA Journal, 41(6):1138–1142. [doi:10.2514/2.2055]
Frýba, L., 1972. Vibration of Solids and Structures under Moving Loads. Noordhoff International Publishing, Groningen, the Netherlands, p.325–333.
Guo, Y.Q., Chen, W.Q., Pao, Y.H., 2008. Dynamic analysis of space frames: The method of reverberation-ray matrix and the orthogonality of normal modes. Journal of Sound and Vibration, 317(3–5):716–738. [doi:10.1016/j.jsv.2008.03.052]
Hamed, E., Frostig, Y., 2004. Free vibrations of cracked prestressed concrete beams. Engineering Structures, 26(11):1611–1621. [doi:10.1016/j.engstruct.2004.06.004]
Howard, S.M., Pao, Y.H., 1998. Analysis and experiments on stress waves in planar trusses. Journal of Engineering Mechanics, 124(8):884–891. [doi:10.1061/(ASCE)0733-9399(1998)124:8(884)]
Jiang, J.Q., Chen, W.Q., 2009. Reverberation-ray analysis of moving or distributive loads on a non-uniform elastic bar. Journal of Sound and Vibration, 319(1–2):320–334. [doi:10.1016/j.jsv.2008.05.031]
Kocatürk, T., Şimşek, M., 2006a. Vibration of viscoelastic beams subjected to an eccentric compressive force and a concentrated moving harmonic force. Journal of Sound and Vibration, 291(1–2):302–322. [doi:10.1016/j.jsv.2005.06.024]
Kocatürk, T., Şimşek, M., 2006b. Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load. Computers and Structures, 84(31-32):2113–2127. [doi:10.1016/j.compstruc.2006.08.062]
Law, S.S., Lu, Z.R., 2005. Time domain responses of a prestressed beam and prestress identification. Journal of Sound and Vibration, 288(4–5):1011–1025. [doi:10.1016/j.jsv.2005.01.045]
Lee, J., Schultz, W.W., 2004. Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method. Journal of Sound and Vibration, 269(3–5):609–621. [doi:10.1016/S0022-460X(03)00047-6]
Pao, Y.H., Sun, G., 2003. Dynamic bending strains in planar trusses with pinned or rigid joints. Journal of Engineering Mechanics, 129(3):324–332. [doi:10.1061/(ASCE)0733-9399(2003)129:3(324)]
Pao, Y.H., Chen, W.Q., 2009. Elastodynamic theory of framed structures and reverberation-ray matrix analysis. Acta Mechanica, 204(1–2):61–79. [doi:10.1007/s00707-008-0012-z]
Pao, Y.H., Keh, D.C., Howard, S.M., 1999. Dynamic response and wave propagation in plane trusses and frames. AIAA Journal, 37(5):594–603. [doi:10.2514/2.778]
Pao, Y.H., Chen, W.Q., Su, X.Y., 2007. The reverberation-ray matrix and transfer matrix analyses of unidirectional wave motion. Wave Motion, 44(6):419–438. [doi:10.1016/j.wavemoti.2007.02.004]
Tse, F.S., Morse, I.E., Hinkle, R.T., 1978. Mechanical Vibrations: Theory and Applications. Allyn and Bacon, Boston, USA.
Yang, J., Chen, Y., Xiang, Y., Jia, X.L., 2008. Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load. Journal of Sound and Vibration, 312(1–2):166–181. [doi:10.1016/j.jsv.2007.10.034]
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Basic Research Program of China (No. 2009CB623204), and the National Natural Science Foundation of China (Nos. 10725210 and 10972196)
Rights and permissions
About this article
Cite this article
Jiang, Jq., Ye, Gr. Dynamics of a prestressed Timoshenko beam subject to arbitrary external load. J. Zhejiang Univ. Sci. A 11, 898–907 (2010). https://doi.org/10.1631/jzus.A1000057
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.A1000057