Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method

Figure 7

The forced responses of a type III two-stage isolator in primary resonance, for , and the corresponding free periodic motions on the approximate NNM invariant manifold for the underlying conservative system. (a) Displacement amplitude-frequency responses for the payload and the ones for the lower stage of the isolator under force excitations with increasing frequency and different amplitude : pink solid line represents ; blue dashed line represents ; green dotted line represents ; red dashed-dotted line represents ; black solid line represents ; the other parameters of the system are the same as in Figure 2. (b) Five representative forced responses in primary resonance of the system shown in different line styles, which correspond, respectively, to the solid points on the curves in (a) with the same color and line style. Five free periodic motions of the underlying conservative system are shown in solid lines. In the neighborhood of each periodic trajectory, the corresponding forced response orbit evolves. (c-d) The approximation of the NNM invariant manifold for the displacement constraint and , respectively; the five free periodic trajectories in (b) are also presented in solid lines in (c) and (d); is the projection of onto the phase space of generalized modal coordinates.

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