The steady-state response of the classic mass-spring-dashpot model when the spring stiffness decays exponentially with time (an aging spring) and the system is excited by a forcing function whose frequency is equal to the natural frequency of the system with the constant initial stiffness is investigated. The steady-state response is obtained in terms of the dumping and decay constants of the system and exhibits an oscillation about a nonzero value.

Issue Section:
Brief Notes
Keywords:
damping, resonance, ageing, Bessel functions, classical mechanics, elastic constants
Topics:
Resonance, Springs, Steady state, Stiffness, Damping, Shock absorbers, Bessel functions
1.
Chen
,
H.
, and
Wu
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T. T.
,
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An Aging Spring
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2.
Wan, F. Y. M., 1976, “Education Notes, Applications of Differential Equations,” Applied Mathematics Note, Vol. 2, Canadian Applied Math Soc., pp. 27–31.
3.
Chopra, A. K., 2001, Dynamics of Structures, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ, Section 3.2.2.
4.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.
Copyright © 2002
 by ASME
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