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
An Aging Spring,”
Stud. Appl. Math.,
Wan, F. Y. M., 1976, “Education Notes, Applications of Differential Equations,” Applied Mathematics Note, Vol. 2, Canadian Applied Math Soc., pp. 27–31.
Chopra, A. K., 2001, Dynamics of Structures, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ, Section 3.2.2.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.
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