Effect of Internal Moment Release on the Eigenfrequencies of Combined Linear Systems
Publication: Journal of Engineering Mechanics
Volume 132, Issue 8
Abstract
A method for analyzing the free vibration of complex structural systems, consisting of a simple oscillator attached to a beam with an internal hinge, is presented. A mathematical model possessing important features of singularity functions with their higher order derivatives is proposed to account for the effect of internal hinge and spring force interacting between the oscillator and supporting structure. The particular integral approach together with Laplace transformation is proved to be an efficient alternative to solve the generalized differential equation for the normal modes of dynamically combined systems. Exact vibration frequencies for clamped–pinned and pinned–pinned boundaries are determined. The results are extended to the cases in which the oscillator or internal hinge is removed from the structure. It is shown that the presence of internal hinge does not alter the generalized orthogonality relation for the combined system. The search for the optimal location of the internal hinge, which maximizes the desired natural frequency, is discussed. It is concluded that a combined system with an optimally positioned hinge vibrates with the same natural frequency as an equivalent system without a hinge.
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References
ANSYS (1994). User’s manual, revision 5.3.
Broome, T. H. (1989). “Economical analysis of combined dynamical systems.” J. Eng. Mech., 115(10), 2122–2135.
Brungraber, R. J. (1965). “Singularity functions in the solution of beam-deflection problem.” Eng. Educ., 55(9), 278–280.
Der Kiureghian, A., Sackman, J. L., and Nour-Omid, B. (1983). “Dynamic analysis of light equipment in structures: Response to stochastic input.” J. Eng. Mech., 109(1), 90–110.
Dowell, E. H. (1972). “Free vibrations of an arbitrary structure in terms of component modes.” J. Appl. Mech., 39, 727–732.
Dowell, E. H. (1979). “On some general properties of combined dynamical systems.” J. Appl. Mech., 46, 206–209.
Friedman, B. (1956). Principles and techniques of applied mathematics, Wiley, New York.
Lee, Y. Y., Wang, C. M., and Kitipornchai, S. (2003). “Vibration of Timoshenko beams with internal hinge.” J. Eng. Mech., 129(3), 293–301.
Liverman, T. P. G. (1964). Generalized functions and direct operational methods, Vol. I, Prentice–Hall, Englewood Cliffs, N.J.
Nicholson, J. W., and Bergman, L. A. (1986a). “Free vibration of combined dynamical systems.” J. Eng. Mech., 112(1), 1–13.
Nicholson, J. W., and Bergman, L. A. (1986b). “Vibration of damped plate-oscillator systems.” J. Eng. Mech., 112(1), 14–30.
Nour-Omid, B., Sackman, J. L., and Der Kiureghian, A. (1983). “Modal characterization of equipment-continuous structure systems.” J. Sound Vib., 88(4), 459–472.
Pesterev, A. V., and Bergman, L. A. (1995). “On vibration of a system with an eigenfrequency identical to that of one of its subsystems.” J. Vibr. Acoust., 117(4), 482–486.
Pesterev, A. V., and Tavrizov, G. A. (1994). “On vibrations of beams with oscillators, I: Structural analysis method for solving the spectral problem.” J. Sound Vib., 170(4), 421–536.
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Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 8 • August 2006
Pages: 823 - 829
Copyright
© 2006 ASCE.
History
Received: Jan 13, 2005
Accepted: Nov 16, 2005
Published online: Aug 1, 2006
Published in print: Aug 2006
Notes
Note. Associate Editor: Joel P. Conte
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