230 T. Detroux et al. Fig. 21.1 Experimental setup. (a) Top view; (b) Side view chords are attached to mass 1 (see Fig. 21.1b) to provide a nonlinear restoring force in the direction of motion. The displacements of the transverse spring supports are prescribed to impart motion to the two masses using a Scotch yoke flywheel [7]. The Scotch yoke converts rotational motion into an unidirectional harmonic displacement d DDsin.!t/. The frequency!=2 was limited to2:7Hz in the present experimental test rig, and the amplitude Dwas set manually, but could be accurately estimated. The restoring force in the system caused by the transverse bungee chords can be theoretically written as [4] Fnl.x/ D2k 0 B @ 1 q1C.x=l/2 1 C A (21.1) where x Dx1 d is the displacement of mass 1 x1 relative to the displacement of the base d, k, l andl0 denote the stiffness, length and natural length of the lateral springs, respectively, and D l=l0 is the pre-stress parameter. The Taylor series expansion of Eq. (21.1) around 0 reads Fnl.x/ D.1 /xC 2l2 x3 CR3.x/: (21.2)
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