Free Vibration of a Generalized Plane Frame

Authors

Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

This article deals with the free in-plane vibration analysis of a frame with four arbitrary inclined members by differential transform method. Based on four differential equations and sixteen boundary and compatibility conditions, the related structural eigenvalue problem will be analytically formulated. The frequency parameters and mode shapes of the frame will be calculated for various values of the structural properties, such as joint angles, springs' stiffness and flexural rigidity of members. Finally, the obtained solution by the proposed method will be verified by authors' finite element program.

Keywords

References

1.     Filipich, C. and Laura, P., "In-plane vibrations of portal frames with end supports elastically restrained against rotation and translation", Journal of Sound Vibration,  Vol. 117, (1987), 467-473.
2.     Kounadis, A. and Meskouris, K., "The coupling effect of axial motion and joint mass on the lateral vibrations of a rigid‐jointed triangular frame", Earthquake Engineering & Structural Dynamics,  Vol. 15, No. 4, (1987), 447-461.
3.     Laura, P., De Greco, B.V. and Filipich, C., "In-plane vibrations of frames carrying concentrated masses", Journal of Sound and Vibration,  Vol. 117, No. 3, (1987), 447-458.
4.     Filipich, C., de Greco, B.V. and Laura, P., "A note on the analysis of symmetric mode of vibrations of portal frames", Journal of Sound and Vibration,  Vol. 117, No. 1, (1987), 198-201.
5.     Chang, G.-S. and Chang, C.-H., "Out-of-plane vibrations of plane frames", Journal of Sound and Vibration,  Vol. 147, No. 1, (1991), 137-154.
6.     Lee, H., Natural frequencies and modes for the in-plane vibration of a triangular closed frame. 1993, Academic Press.
7.     Lee, H. and Ng, T., In-plane vibration of planar frame structures. 1994, Academic Press.
8.     Aktas, E. and Moses, F., "Reduced basis eigenvalue solutions for damaged structures∗", Journal of Structural Mechanics,  Vol. 26, No. 1, (1998), 63-79.
9.     Oguamanam, D., Hansen, J. and Heppler, G., "Vibration of arbitrarily oriented two-member open frames with tip mass", Journal of Sound and Vibration,  Vol. 209, No. 4, (1998), 651-669.
10.   Sophianopoulos, D., "The effect of joint flexibility on the free elastic vibration characteristics of steel plane frames", Journal of Constructional Steel Research,  Vol. 59, No. 8, (2003), 995-1008.
11.   Lin, H. and Ro, J., "Vibration analysis of planar serial-frame structures", Journal of Sound and Vibration,  Vol. 262, No. 5, (2003), 1113-1131.
12.   Heppler, G., Oguamanam, D. and Hansen, J., "Vibration of a two-member open frame", Journal of Sound and Vibration,  Vol. 263, No. 2, (2003), 299-317.
13.   Mei, C., "In-plane vibrations of classical planar frame structures—an exact wave-based analytical solution", Journal of Vibration and Control,  Vol. 16, No. 9, (2010), 1265-1285.
14.   Kaveh, A. and Aalizadeh Arvanaq, R., "Free vibration of symmetric planar frames via the force method and canonical forms", International Journal for Numerical Methods in Biomedical Engineering,  Vol. 27, No. 6, (2011), 936-961.
15.   Rezaiee-Pajand, M. and Khajavi, R., "Vibration analysis of plane frames by customized stiffness and diagonal mass matrices", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,  Vol. 225, No. 12, (2011), 2848-2863.
16.   Şakar, G., Öztürk, H. and Sabuncu, M., "Dynamic stability of multi-span frames subjected to periodic loading", Journal of Constructional Steel Research,  Vol. 70, No., (2012), 65-70.
17.   Mei, C., "Free vibration analysis of classical single-story multi-bay planar frames", Journal of Vibration and Control,  Vol. 19, No. 13, (2013), 2022-2035.
18.   Yucel, A., Arpaci, A. and Tufekci, E., "Coupled axial-flexural-torsional vibration of timoshenko frames", Journal of Vibration and Control,  Vol. 20, No. 15, (2014), 2366-2377.
19.   Ratazzi, A.R., Bambill, D.V. and Rossit, C.A., "Free vibrations of beam system structures with elastic boundary conditions and an internal elastic hinge", Chinese Journal of Engineering,  Vol. 2013, (2013).
20.   Failla, G., "An exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping", Journal of Sound and Vibration,  Vol. 360, (2016), 171-202.
21.   Rezaiee-Pajand, M., Sani, A.A. and Hozhabrossadati, S.M., "Application of differential transform method to free vibration of gabled frames with rotational springs", International Journal of Structural Stability and Dynamics,  Vol. 17, No. 01, (2017), 1750012.
22.   Rezaiee-Pajand, M., Sani, A.A. and Hozhabrossadati, S.M., "Free vibration analysis of a six-degree-of-freedom mass-spring system suitable for dynamic vibration absorbing of space frames", International Journal of Engineering-Transactions A: Basics,  Vol. 30, No. 1, (2016), 30-39.
23.   Albarracín, C.M. and Grossi, R.O., "Vibrations of elastically restrained frames", Journal of Sound and Vibration,  Vol. 285, No. 1-2, (2005), 467-476.
24.   Grossi, R. and Albarracín, C., "A variational approach to vibrating frames", Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,  Vol. 221, No. 2, (2007), 247-259.
25.   Grossi, R.O. and Albarracín, C.M., "Variational approach to vibrations of frames with inclined members", Applied Acoustics,  Vol. 74, No. 3, (2013), 325-334.
26.   Chang, C., "Vibrations of frames with inclined members", Journal of Sound and Vibration,  Vol. 56, No. 2, (1978), 201-214.
27.   Kounadis, A., "Bending eigenfrequencies of a two-bar frame including the effect of axial inertia", AIAA Journal,  Vol. 23, No. 12, (1985), 2000-2002.
28.   Rao, S.S., "Vibration of continuous systems, John Wiley & Sons,  (2007).
29.   Hozhabrossadati, S.M. and Sani, A.A., "Free vibration of mdof systems with nonperiodically time-varying mass", International Journal of Structural Stability and Dynamics,  (2017), 1850077.
International Journal of Engineering
Volume 31, Issue 4
TRANSACTIONS A: Basics
April 2018
Pages 538-547

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