Generalized orthogonality condition for beams with intermediate lumped masses subjected to axial force

JVC/Journal of Vibration and Control

Volumn 16, Issue 5, 2010, Pages 665-683

  Hassanpour, P A ^a   Esmailzadeh, E ^b   Cleghorn, W L ^a   Mills, J K ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY   (Canada)

Author keywords

Axial force; Beam; Exact mode shapes; Orthogonality condition

Indexed keywords

AXIAL FORCES; BEAM MASS SYSTEMS; COMPUTATION TIME; DAMPING MATRICES; DIFFERENT BOUNDARY CONDITION; DISTRIBUTED PARAMETER SYSTEMS; DYNAMIC BEHAVIORS; GENERALIZED ORTHOGONALITY; LUMPED MASS; MODE SHAPES; ORTHOGONALITY; ORTHOGONALITY CONDITIONS; ROTATIONAL SPRING;

AXIAL FLOW; BOUNDARY CONDITIONS; DAMPING;

DYNAMIC RESPONSE;

EID: 77951103933     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546309106526     Document Type: Article

References (16)

1. Boyce, W.E. and DiPrima, R.C., 2005, Elementary Differential Equations and Boundary Value Problems, Wiley, Hoboken, NJ.
2. Chang, T.P., 1993, " Forced vibration of a mass-loaded beam with a heavy tip body, " Journal of Sound and Vibration 164, 471-484.
3. Hamdan, M.N. and Jubran, B.A., 1991, " Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia, " Journal of Sound and Vibration 150, 203-216.
4. Hassanpour, P.A., Cleghorn, W.L., Esmailzadeh, E., and Mills, J.K., 2007, " Vibration analysis of micro-machined beam-type resonators, " Journal of Sound and Vibration 308, 287-301.
5. Karnovsky, I.A. and Lebed, O.I., 2004, Free Vibrations of Beams and Frames-Eigenvalues and Eigenfunctions, McGraw-Hill, New York.
6. Kirk, C.L. and Wiedemann, S.M., 2002, " Natural frequencies and mode shapes of a free-free beam with large end masses, " Journal of Sound and Vibration 254, 939-949.
7. Kukla, S., 1994, " Free-vibrations of axially loaded beams with concentrated masses and intermediate elastic supports, " Journal of Sound and Vibration 172, 449-458.
8. Low, K.H., 1997, " Comments on ĝ€Non-Linear vibrations of a beam-mass system under different boundary conditions (with authors reply), " Journal of Sound and Vibration 207, 284-287.
9. Meirovitch, L., 2001, Fundamentals of Vibrations, McGraw-Hill, New York.
10. Ozkaya, E., 2002, " Non-linear transverse vibrations of a simply supported beam carrying concentrated masses, " Journal of Sound and Vibration 257, 413-424. (Pubitemid 35466605)
11. Ozkaya, E. and Pakdemirli, M., 1999, " Non-linear vibrations of a beam-mass system with both ends clamped, " Journal of Sound and Vibration 221, 491-503. (Pubitemid 129550520)
12. Salarieh, H. and Ghorashi, M., 2006, " Free vibration of Timoshenko beam with finite mass rigid tip load and flexural-torsional coupling, " International Journal of Mechanical Sciences 48, 763-779.
13. Sochacki, W., 2008, " The dynamic stability of a simply supported beam with additional discrete elements, " Journal of Sound and Vibration 314, 180-193.
14. Wiedemann, S.M., 2007, " Natural frequencies and mode shapes of arbitrary beam structures with arbitrary boundary conditions, " Journal of Sound and Vibration 300, 280-291.
15. Wu, J.S. and Huang, C.G., 1995, " Free and forced vibrations of a Timoshenko beam with any number of translational and rotational springs and lumped masses, " Communications in Numerical Methods in Engineering 11, 743-756.
16. Wu, J.S. and Lin, T.L., 1990, " Free vibration analysis of a uniform cantilever beam with point masses by an analytical-and-numerical-combined method, " Journal of Sound and Vibration 136, 201-213.