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

Figure 9

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 harmonic force excitations with 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 system parameters are the same as in Figure 2. (b) Five representative forced responses in primary resonance of the system are 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 corresponding free periodic trajectories of the underlying conservative system are shown in solid lines, and they are also presented in (c) and (d) for different phase space. (c-d) The approximation of the NNM invariant manifold for the displacement constraint and , respectively. The parameters set in the numerical solution procedure are , with equally sized elements in the domain , and .

(a)

(b)

(c)

(d)