Forced Vibration in Nonlinear Systems With Various Combinations of Linear Springs

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Abstract
This paper deals with a single mass system containing a combination of linear springs having a force-displacement characteristic as shown in Fig. 1b. By varying the ratio k1/k2 of the spring constants, various modifications occur, e.g., for k1/k2 = 0 there is only one set of springs, and the system has a clearance x0 on each side of the equilibrium position; for k1/k2 = ∞ there is again a single set of springs which is now given an initial set-up force F. The steady-state motion of these systems under the influence of a harmonic external force is wanted. Detailed exact solutions have been published for the cases k1/k2 = ∞ and k1/k2 = 0. In this paper these two special cases have been brought down to a simpler form, and two additional cases (k1/k2 = 2 and k1/k2 = 0.5) have been calculated. All these results, together with those of the classical linear case k1/k2 = 1 are shown in Figs. 5 to 9, inclusive, plotted in two different dimensionless forms.

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