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

Figure 3

The forced responses of a type III two-stage isolator in primary resonance, for and , and the corresponding free periodic motion of NNM invariant manifold for the underlying conservative system. The other parameters of the system are the same as in Figure 2. (a) Displacement amplitude-frequency responses for the payload and the responses for the lower stage in a type III two-stage isolator. (b) The representative forced response in primary resonance of the system is shown in black dot-dashed line, which corresponds to the square points on the curves in (a). The free periodic motion of the underlying conservative system is shown in blue solid line. The corresponding forced orbit occurs in the neighbourhood of this free motion. (c) The approximation of the corresponding NNM invariant manifold for the displacement constraint and the free periodic motion from (b), shown as blue solid curve. (d) The approximate NNM invariant manifold is the projection of onto the phase space of generalized modal coordinates. The free periodic motion in (c) is also projected on this phase space as blue solid line.

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